I don't think there are many characters aside from other Pokémon that hurt our chances. Not sure why a third-party would hurt us. Even if we got something like Digimon, I don't think we'd really be effected. Joker didn't seem to harm the chances of other JRPG characters, did he?
Doesn't appear to be many characters who would help our case outside yet another first-party character from a Switch game. At the very least, it'd further establish the trend of them picking characters from their most recent titles.
As for whether or not either of these last two characters will be first-party, who knows? I've been hearing, "I think there might not be any more first-parties," since Joker, so I'm not particularly fazed by what the community thinks is likely. I also don't think there's any merit to, "It missed its chance," when we have not one, but two characters from games that were roughly three years old by the time their character was added.
If a SwSh Pokemon doesn't get in, it'll because they didn't want one as much as other characters. Simple as that.