I got in the mood for swap so here's more of my take on underswap since y'all liked my swap papyrus take so much.
This is more of a general info for some of the characters so far.
Frisk is constantly tired and cautious so chara guides them and shows them the underground isn't horrible and all they need is kindness. Flowey is the equivalent of >:3 and uses humor and putting down others to cope with the "lack of feelings." Which is partially due to him as asriel just bein a cool kid, so as floweys hes like "im rude now" but depression.
Asgore is ignored and basically void of leadership amd left in the castle chambers to his flowers as he recieves each human soul he didn't want after they're killed. Some of them from Toriel in the ruins, trying to get her people out of here as fast as possible and in remorse for her childrens deaths.
You already know about papyrus from this post, but sans could be expanded upon. He works many different jobs and is very positive despite being a workaholic, always trying to keep a smile on his younger brothers face despite their dilema. When he does take breaks he's at Grillbys for a quick bite, the patrons think he's strange but lovable. (Hes done the "whats up pussycat joke at least once on the juxebox there.) Sans also is a bit more open about his science knowledge in this, "the future is now!" And all that. He still hangs out with alphys. He is still "the judge" but will feel horrible about it during the fight and truly spares you towards the end. "Anyone can change if they just try!"
Mettaton and napstablook are interesting. Mettaton still has his body in this and goes on stage and performs, mostly music. But behind the curtains he's horribly anxious and full of stagefright. Mettaton still wants the body for trans reasons but hates performing in front of everyone, he only does it for that and Napstablook. Towards the end Mettatons confidence is restored after a heart to heart with his cousin, alphys, and the fans. Afterwards napstablook gets a body as well (napstaton) and they perform together on the surface.