Since I have free time, a love for Percy Jackson, a nascent obsession with Genshin Impact (to the point that I spoiled the entire story and I'm barely in Liyue, finishing Act I, so I'm sorry if it's inaccurate with canon) and a very crazy head that won't leave me alone until I get this out of my head, here is my fanart combining GI x PJ.
Starting to present the characters and the lore that I invented, there is Dionysus, who would be Venti with some changes. Before Dionysus, there was Hermes as the first anemo archon (I couldn't leave out my middle child) Dionysus got the position just a few years after Hermes, who died in the war against Khaenri'ah by orders of Celestia (which here would be Kronos), Dionysus never got to meet Hermes, but he did learn his stories from the winds as soon as he became archon Also Dionysus being the god of madness, I definitely see him as someone who would encourage Monstadt to live as freely and happily as possible, and he is also the reason why Monstadt's parties and festivals are so legendary throughout Teyvat.
On the other hand, the next archon is Apollo, geo archon for several, several reasons... (I blame every post on ao3 and Tumblr by @apollosgiftofprophecy and @tsarinatorment, they put a love for Apollo and mythology in me that I appreciate, except here because I thought more about Apollo than mythology half of the characters XD)
First Apollo has some control with Zeus regarding law and order, god of civilization, and is in some way seen as the protector of tombs and cemeteries, it is wonderful that Zhongli (archon Geo in Genshin Impact) works in a funeral home, is related to the law as the god of contracts and has watched over Liyue and its inhabitants, having great influence on its people and how it grew as a civilization In addition to that he also has some influence on sailors and ships, as the patron of sailors, so Liyue being a port city, well discarded and taken Apollo was Zhongli's turn As also the god of knowledge.
I love being a rat so he is the only living archon in this UA who went through the war of the archons, Khaenri'ah and until today, who would take the role of Guizhong would be Jacinto naturally (dead, shipped with Zhongli / Apollo) and who would take the role of Xiao would be Nico di Angelo (dwarf, traumatized... is perfect) plus I can keep the dynamic of Dionysus as Nico's therapist (something that is a little different from canon, Xiao does not receive therapy from Venti, but rather he purifies him) but that would remain as a separate thing from their relationship Also, as an extra Zhongli reviews the future of Liyue to bring a guide on how to prosper (Apollo and his mastery of prophecy), for certain reasons (Artemis) is that he would decide to retire as archon and continue working at the funeral home discreetly with Nico, occasionally hanging out at the orphanage with the children.
Respect to Artemis I will talk about her in her fanart, and her relationship with Apollo along with what happened here
Nico on his side has been with Apollo since the war of the archons, as his right hand (previously he had other companions, similar to the adeptus who serve Rex Lápiz) the most notable is Commodus, who went crazy killing corrupt gods, beings of the abyss and the cherry on top was Apollo's rejection for his feelings, still hurt by the death of Hyacinth (with whom unlike Guizhong, he would be god of flowers) but they would have spent almost as much time as Zhongli and Guizhong together (close to 1000 years if I'm not mistaken, I appreciate the corrections) so he would continue fighting with a broken heart.
(PS: I also thought of Branchus as Guizhong but, Guizhong fell in the war, Hyacinth did not die a peaceful death then... well, tragedy with tragedy).
Continuing with Nico, he would be mourning for his companions but with Apollo they decided to take it easy, and he was in Apollo's retirement plan (who says that with stone and an archon's influence you can't make a fake corpse?) and he has been improving with the mourning and trauma of the war with the help of Dionysus and the passage of time.
Lastly Meg, because she is the strongest daughter of Demeter she couldn't just be left as an extra, no, no, no.
I understand than Neuvillette is the hydro dragon reborn as her own offspring, here Meg would be the remains of the essence of Demeter, discovered by Artemis who thought she was a child of an endangered species and raised her, when what happened with Artemis happened (the same as with Rukkhadevata, but whoever reads this and is part of the PJO fandom will not know) Apollo took her under his custody with Nico and now she works with them, apart from living with them, in the funeral home .
Speaking of the designs, I tried to make the clothes as faithful as I could, Apollo with Liyue clothes, some Greek and Sumeru for his sister (the moon earring that he has is Artemis's), with white eye shadow (also for his sister that I designed with white locks), a book, a random kid from the orphanage with long hair in a braid (courtesy of Meg who wanted to practice and Nico doesn't let him).
Nico with long hair (because he lived with Apollo for so long he started to like to wear his hair a bit long, also in reference to ancient China and the custom of not cutting his hair), his usual dark circles and his hidden vision on his back.
Meg with a Sumeru bird (coincidentally called Peaches) somewhat more Sumerian clothes and a spear, she is trying to learn to fight with other weapons apart from her classic twin swords.
And Dionysus with a good bottle of Dandelion Wine, classic from Monstadt, and more Monstadt clothes too.