Honestly? I just want the reverted character and environment designs from the TTYD remake to stick, instead of just resuming the post-SS redesigns. Yeah, that's a little shallow, but I want my thick-browed goombas and female-presenting toads. And child/elderly toads. And the RPG-original races like Doogans and Shamans. And Toadsworth. ...And having a taste of them back again after so long just makes me anxious to lose them again.
While I'd of course want a new Paper Mario to build on the 64/TTYD gameplay style, I think it is fair to say that Origami King was a pretty decent title in the sense that it had some interesting ideas that could've really gone somewhere if they'd been totally fleshed out instead of being at a weird halfway point where it was clearly trying to emulate some of the older ideas while still insisting on being different.
Battles in particular. I actually really liked the boss battles in Origami King, looking back on it. Some of them had pretty hectic vibes, and having them essentially be puzzle-fights had some genuine value. Regular battles, though? While they were okay-ish, they were still held back by forced limited attack resources and lack of major/permanent rewards. Oddly (or perhaps not so oddly, given the insistently different-from-before vibes most earlier Switch titles had), I think I feel the way about them that I feel about BoTW's battles. They had the potential to be fun, and sometimes really were, but after a while I just started avoiding any non-mandatory ones because it felt like they weren't particularly meaningful, and really just ended up using limited battle resources I knew I'd have to buy more of - and it just became a 'buy items-use items-get coins-buy items' loop without any sense of progression beyond different areas selling different items. But maybe that's just me.
I think if they're going to try out a different gameplay style with Paper Mario, they need to fully lean into it the way that Super did, by being a sort of action-RPG with a platformer focus. If the next Paper Mario wants to lean more into puzzle/adventure, maybe they could just take it all the way and turn it into something similar to the pre-BoTW Zelda games.