Maybe some people see Yugi as the more codependent one in the context of him and Yami/Atem, whether platonic or romantic or anything in between.
But... I don't believe that he is. Because if you're so codependent of someone... You wouldn't actually remind yourself of who they are, which is a far distict person from you.
After the fire, Yami tries to tell Yugi about what he KNOWS, the little that he does, which is significant with his lack of memories. But it isn't unprompted.
Yugi asked him. Because Yami Bakura told him this during the game with Ryuji.
The fact that Yami doesn't even know his own name... Makes all the color drain from Yugi's eyes. Dread is all over his face and it settles in, because deep down he already knows the answer.
When Atem/Yami tries to tell him where his journey should go, and that maybe, just maybe he will regain his memories, Yugi... Dismisses it entirely. He tries to push past it.
Yugi isn't just ignoring how Yami feels.
Yugi is just scared. And we already know why.
Yugi already chose death once. He chose to die with Yami. He chose to see him one last time and die together.
And Yami knows it too. Yami has started to see what was happening, and why he thanks him for saving him. (Which Yugi mentions Jounouchi saved him :'))
Yugi is scared, because Yami will go somewhere where he can't go. He will die, but he cannot die with him. He's scared of losing him.
It makes sense why Yami chose to say what he said. In a way, he wants to stay too, so nothing like that will ever happen again.
But he also wants to know who he is.
And Yugi... Already suspects this. He already knew that something connected to Yami, to their puzzle, will occur.
That look of recognition is obvious. And then, it's obvious why all the color drains from Yugi as Yami tells him he doesn't remember anything.
We were already shown in DDM, that Yugi can pick up on finer details in a quick manner to react when he doesn't have much time, so it's easy to parallel that with this scene.
And once again, the date after this? Yugi set him and Anzu up to it. It was his idea, though in a way he wished to live through Yami as well with how he dressed.
What's interesting though... It's that Yugi's and Anzu's parts are parallels. Yami approaches them both the same manner.
He probably expects Anzu to dismiss it the way Yugi did.
And it shows that he's at conflict inside, which Yugi could tell it was SOMETHING, hence the date, and Anzu... Is right. Yugi is tough. She is being considerate to who Yugi wants to be, who he is, an individual separate from the spirit of the puzzle.
Which is something that begins to show not long after this.
He's asking Anzu to keep it a secret, not knowing that Yugi already has a inkling, but more importantly, a more striking detail...
Yugi knows about the museum exposition. Yami knew where to go because Yugi knew.
If Yugi was so codependent... Pray tell, why does he say these things?
We have already seen Yugi casually win games before. He's pretty happy doing that, especially in a fighting video game. Sure, he might feel bad and even belittle himself for being selfish, but he wouldn't turn it down entirely.
Yami is pretty happy with his wins, too. But this feels like a distinct belief between the two: Yugi is fine with a ante, it's like in poker, or any other game that you can put an ante on, but Yami isn't, because for Duel Monsters you can't evaluate the rarity of a card to each and every duelist.
Yugi may not know why Yami is fighting in this battle, but he knows that it isn't greed or glory. Which makes him conclude it must be something else.
And even after he tells Yugi that he fights to find himself, Yami doesn't tell him about the visit and about Ishizu. (Who Yugi saw in the paper)
So Yugi may not know the full reason, and maybe Yami feels Yugi isn't ready to hear the full answer just yet...
...But Yugi trusts him. And doesn't stop him from looking for what he wishes. He actively reinforces it. He will help him find that answer. He won't hinder him.
A sentiment which is reflected later in the mime duel, Yugi can't hide behind him forever, he needs to grow stronger, stronger than even Yami himself, strong to stand on his own.
Someone that codependent wouldn't actively fight against the desire to hold onto someone and isolate them, ignore every one of their wishes and keep them stagnant.
Which is what I love about Yugi.
Because... He and Yami are now parallels. They are BOTH struggling with these emotions, stuck between "I want to stay with you" / "I want to know who I am"
Yugi knows Yami will need to fight in something big, he knows he will be involved because of the Necklace, but he doesn't want Yami to die, not after they both early did, not after he made a choice.
But he also starts to show that he wants to grow, to express and be himself. After so long of not being heard, finally being heard by Yami during the Pegasus duel seems like his biggest achievement yet. They can talk now, they can be friends, they can get to know each other better.
And Yami, he desperately wants to know who he is, where he comes from, what his purpose is, but he also wishes to stay with Yugi, who risked limb and bone to save him, who he's indebted to endlessly, who has helped him defeat Pegasus.
We are shown more of Yami's side, but we can infer from it based on Yugi's reactions around the issue.
Because Yugi hasn't forgotten that talk on the hospital roof. Yes, he pushed it down, but he hasn't forgotten it entirely, and it shows (heck he even feels guilty for having pushed it down/out of his mind briefly), because it was HIM who asked YAMI. If Yugi never talked... If Yugi never asked...
...would Yami have tried telling him? Would Yami have tried looking for answers? We aren't shown a hint that he would've mentioned anything prior to Yugi asking, he was simply enjoying the sight with him.
If Yugi hadn't set him up with Anzu... Would Yami have had the courage to find these answers? Anzu gave him the push he needed...
...but it was Yugi who set it all in motion to begin with. Which is often overlooked.
Which also speaks of how Yugi knows Anzu, too, aside from the crush. He knows she's strong, and that she won't just walk around the issue, that she will meet him head-on.
When she stood up to him in the very first chapter, after Jounouchi and Honda were gone, she told him to learn to stand up for himself more, rather than be a pushover for the others.
It shows she wants him to grow, and he hasn't forgotten that. Plus, talking to her about his treasure at the time made him feel better.
Not a stretch that he nudged Yami towards Anzu, ofc she should be able to make him feel better.