I also think it's going to be a first party. It's been a steady progression down to this point. It would narrow down the options it could be, but that doesn't make it any easier. Many of them have factors you could say against them, whether that's Assist Trophy, Spirit Event, or already repped in Ultimate. The ones without any of that seem much more unlikely, but that's subjective.
In the end I've just tried to think about what Nintendo would pick and narrowed it down to these three, though it's still carrying a bit of bias. I've put points for and against, but these don't all matter and you can easily explain them away to be honest.
Pokémon Gen 8 - I don't want this, but its such a Nintendo pick. Points for: It's the biggest franchise in the world, Gen 8 isn't in yet. Points against: Gen 7 rep in Ultimate, Sw/Sh spirit event, series well represented.
Isaac/Felix - Obviously my top choice. Points for: New series fighter/stage, ballot pick, lots of content. Points against: Assist Trophy, no sign of new game, many JRPGs already in DLC.
Waluigi - Don't really care for him but it would be funny. Points for: Crazy popular, meme status. Points against: Assist Trophy, no base game/not much content, series well represented.
Honourable mentions go to Paper Mario or a Zelda rep. While they don't have much in the way of barriers, it feels like they're in a weird spot at being left this long. Paper Mario would feel kinda late, and a 3rd Mario might not be super well received. BotW trilogy only has one or two contenders and they'll be quite new. The classic Zelda characters that get demanded are all assist trophies, and I'm confident my picks above are more popular.
Still not confident in this though, they could break the pattern and drop a big third party. Who knows at this point. I'll keep my fingers crossed for Isaac until the end.