Whether canon provides input on them or not.

During their first interaction on screen in the main story, Madoka Kaname and Sayaka Miki are being introduced to the viewer as classic "Magical Girl" trope(s): The childhood best friends, super close, mutually caring - with slight homosexual subtext, which, at this point in time, might be both, lighthearted fun (teasing) and subtle foreshadowing, but we will get to that. Madoka appears to be the more shy, timid one among the two, whereas Sayaka is more spunky, energetic. If their relationship was a meme, Sayaka would be the one to say "She asked for no pickles, sir!" while standing in front of Madoka to shield her, which may seem simple enough as a dynamic at first glance. However - once again, this may be very subtle foreshadowing towards their future roles in the story as well.

How, you may ask? Well, Sayaka doesn't only joke around wanting "someone like Madoka" as her "wife", she also acts as a protector of Madoka, ever since they were small children - almost like a knight would. A Knight to a Princess or, maybe even... A Goddess? But we're getting ahead of ourselves.

Madoka and Sayaka start off as equally clueless about the whole Magical Girl system - upon meeting Mami for the first time, they're both fascinated and enchanted by her and the idea of getting a wish granted. Not only that, but it'd also mean to then accompany Mami on her duty to fight for justice. However, they're also both hesitant at first - not only because of Homura's mysterious antagonism or Mami literally warning them about contemplating their wishes carefully. Not being fully aware of the full consequences yet, they're both on the same page of not knowing what exactly to wish for - they're aware of how lucky and sheltered they both are... Unfortunately, their hesitation ends up being punished, as they have to witness Mami's death without being able to do anything about it, thus suffering from heavy survivor's guilt afterwards.

At this point, instead of moving forward together, they slowly but steadily start to divert from one another - because their view on the Magical Girl business from then on is influenced by different angles: Madoka, who saw Mami's weak side and loneliness, fears to take a wrong step forward with the wrong intentions, but is also unable to tell Sayaka about it. Sayaka on the other hand idealizes Mami as a beacon of perfection to a point of wanting to become her replacement - despite knowing that she has to pick her wish carefully, especially once it is made for another person, she goes for it. And, at the same time, she reassures Madoka not to worry about it, that she doesn't have to make the same sacrifice, as Sayaka will provide for them both. To fight as Magical Girl, as a righteous knight with a sword - for her wish, for her love, for Mami's sake. And for Madoka's.

But once Kyouko enters the picture - things start to go downhill for Sayaka. Not only does she feel like she has to fight both Witches AND the likes of selfish Magical Girls like Kyouko and Homura; not only is she being told that her potential is not as great as Madoka's, so she has to work twice as hard; not only does her wish backfire on her as she has to realize "not to be human" anymore, unable to make a move towards the boy she loves and getting in the way of the friend who fancies him as well; she eventually starts to spiral, becoming more and more frustrated, depressed, tainted... Until she snaps at Madoka, calling her a coward for not fighting herself, for not supporting her... And hating herself even more for holding it against Madoka.

Madoka, who feels powerless and helpless, unable to move, unable to get on the same page as Sayaka - until it's too late and the extent of Sayaka's despair turns her into a Witch. Even if Madoka joins Kyouko's attempt to bring her back to her senses, hoping that her best friend's voice may have an impact... It's all in vain in the end.

It's only when Madoka finally makes her wish - it's when she decides to end her own existence as a person to become a Concept to erase all Witches from existence, that she also sees the extent of Sayaka's suffering. Once turned into Madokami, the Law of Cycles, rewriting the universe - she is able to finally act, to save Sayaka from her fate of becoming a Witch, telling her that her wish was never for naught... And thus, they leave the mortal world, the universe of Wraiths without Witches, together, leaving behind all regrets.

Fasting forward to Rebellion, we actually see Sayaka acting as a true knight for Madokami's sake - acting almost as an (at some point) enlightened soldier alongside Nagisa in the Witches' Labyrinth of Homura's Soul Gem to bring Homura to her senses and take her away with them to Madokami as well. Only for things to eventually turn out for the worst again - having Homucifer create a new universe, a deceiving, fake world in which both Madoka and Sayaka can live as normal humans once more. Question mark?

... And this is, more or less, what's written in the text about them. Of course there are more interactions between these two, minor or more meaningful, in various pieces of media, such as the PSP game and the Magia Record anime. Overall, their dynamic can be summed up as follows: As mentioned in the beginning, they are childhood best friends with a mutually protective attitude - however, the extent of HOW they protect each other changes through the course of the series. As Sayaka is a little more proactive while Madoka is more hesitant at first, a rift begins to form between the two - Sayaka claims to want to fight for everyone's sake, but as much as she would want to spare Madoka from having to fight herself, she feels the increasing burden of loneliness herself, unable to open up about it, unable to confess her weakness, her more "ugly" side until she snaps. Throughout the main story, Sayaka's state is constantly at the back of Madoka's head - she condemns herself for being so weak and hesitating, having to watch everyone wither away one after another until she finds the courage to make the most selfless wish and save everyone, including Sayaka, in her own way.

While both of them have a multitude of reasons that motivate their actions, they do have each other's well-being in mind a lot. As best friends who have known each other long before the events of the story take place, there is a sense of familiarity and fondness between the two - one that, unfortunately, gets tested by the circumstances they find themselves in, revealing that they may not have felt as equals for a long time. And so, just like basically every other relationship in the series, they happen to be doomed by the narrative.

In general, Sayaka "jumping ahead" of Madoka and, unintentionally, "leaving her behind" is a theme as well. The Different Story is probably the most "in your face" about it, as Madoka confesses to Kyouko that she always "followed Sayaka's tail", was always protected by her; that she found Sayaka cool and wanted to be like her - but also be useful. So once Sayaka became a Magical Girl before her in this timeline as well, she felt like she grew more and more distant from Madoka, becoming closer to Mami instead. Once again, Madoka isn't brave enough to make a move - and it's only when she eventually promises Mami to replace her as a Magical Girl, wishing for Sayaka to come back to life, that she seems to be able to reconcile with Sayaka.

Sayaka may or may not even be aware of how, despite her determination to protect Madoka, she tends to drift towards other people more easily. The PSP game basically confirms that Sayaka is drawing strength from being physically close to Madoka - yet either she denies herself that closeness (like in the main story) or becomes closer to other people instead (like Mami in The Different Story and Magia Record, Kyouko in Rebellion, etc).

Long story short: They are incredibly, irrevocably important to one another, but may not always have the means to stand beside each other as equals for most of the timelines. Either Sayaka jumps ahead of Madoka in becoming a Magical Girl and, despite the best intentions, may grow closer to other people. (In the pre-story timeline in which Mami and Madoka are an established Magical Girl duo, it's the other way round: Sayaka is nowhere to be seen.) Or they finally realize what they did for one another in all timelines after gaining awareness as Madokami and Enlightened!Sayaka (or LawOfCycles!Sayaka, as I called her in the other analysis posts). But in the end, they are STILL somewhat on different levels as a Goddess and her Knight.

Whether I think why and how they’d work.

If you were like me and watched the first episode back then, Hitomi's comment "But you're both girls! This is forbidden!" may have set the tone of the series for you too. As implied, this may or may not be taken as subtle foreshadowing towards the gay (sub)text of the series and the inherent queerness of the Holy Quintet as a whole... And it may also have made you want to see how and if MadoSaya might develop further. After all, Sayaka's comment on how she'd want to take Madoka as her wife has to mean something - at least in regards of her own bisexual tendencies. Right?

For me personally, the way I have outlined their dynamic above leads me to believe that A LOT of things have to go right for them to get together romantically. Just like every other ship within the Holy Quintet, it'd require copious amounts of communication and actually opening up to one another; in this case specifically, they NEED to be on the same page about their intentions and what it'd mean to them to feel on equal grounds. Of course you can be mutually protective - but you gotta be intentional about it, meaning, you cannot act for the other without letting them in. Sayaka cannot always take the lead, she has to let Madoka make her own decisions - and Madoka needs to put her foot down.

They might be more likely to actually make it work, because they already have a solid connection from the very beginning; they care about and value each other to the core after all! However - depending on the timeline, they both tend to somewhat gravitate more towards other people. For example, they're both equally fascinated with Mami, but once one of them gets closer to her than the other - things tend to get imbalanced. Which may or may not require a polycule after all, but I digress. Then there's also their aforementioned "hierarchical difference" as Madokami and Enlightened!Sayaka; on one hand, it's a beautiful (if not a little tragic) depiction of their mutual devotion and loyalty, which has its own appeal. But on the other hand, it may - or may not - put a drift between them once more. Granted, their selves in Homura's Witches' Labyrinth may have been tainted by Homura's own ideas and preferences to a certain degree - but Sayaka is definitely closer to Kyouko here, whereas Madoka is to Homura.

In the end, I feel like they would actually have a fair chance to fall for each other in a world without Magical Girls - because in a world where it's just them, where Sayaka may never gather the courage to move towards Kyousuke, she may have the space to explore her feelings towards the same sex more thoroughly. And being as close to Madoka as we see them being at the beginning of the main story - why shouldn't she allow herself to actually fall for her? Her best friend, whom she always felt like the protector for - and maybe, the whole "wife" joke wasn't a joke after all? It may allow her to see Madoka grow up to become more confident. Madoka, who'd learn to choose for herself, to realize that her adoration for Sayaka had been the first glimpse of romantic affection, learning to let herself be in love with her as well... In a world where they don't have to risk their lives or have their circumstances be tampered with by external forces. Even if it means not meeting Mami, Homura or Kyouko... It'd be their chance to find happiness together.

Whether I’d prefer them as platonic or romantic ship.

I'm usually a huge fan of the "best childhood friends to lovers" trope - and while there is a huge sense of commitment between these two that makes them appealing, I mostly enjoy them as platonic best friends.

On the other hand, I saw a meme the other day that perfectly summarized my romantic stance on them: "They strike me as the kind of people who promise to marry each other if they both turn 40 and still aren't taken." Granted, this scenario would require a timeline where they are actually allowed to grow up, but... Let's, theoretically, assume we'll get an ending post-Walpurgisnacht Rising, where, potentially, Homura may never have become a Magical Girl and/or interfered with everything (because she may voluntarily have chosen to take herself out of the equation)... A KyouMami + MadoSaya ending might be an interesting variation.