On the bright side, we're officially a week away from the anniversary of the last Nintendo Direct.
Yay....?
This is indeed a bad thing as other people already said; anyway, let's think about how even before covid, we have been half year without a general direct. This is IMO the sign that Nintendo is changing their way to do announcements, and that the Directs are not their favorite method anymore (not the general ones at least).
Anyway, not based on anything, just what I feel, I think that the next character will be teased around mid september and released around end of october/beginning of november; but a september announcement with "avaliable now" might also happen too, it's just less likely IMO. The character after will probably be teased in late december and released the next year similar to Joker in FP1.
As unlikely as it may seem, I think that it will probably be a first party once again. Most of the times, third parties were leaked in a way or another. With Byleth they were able to keep the secret until the end, and with min min kinda too, more or less. It seems that it's easier to avoid leaks when the character is first party because they have more control over the informations; this is why I think that the next character is likely another first party (or second if not first). What franchise I don't know... Some of the possible ones are Pokèmon, Kirby, Zelda, DK (basically just Dixie), Rhythm Heaven; but I don't know really.
It can still be third party though, maybe they just became better at keeping their stuff secret and first or third party doesn't matter at all.
This can be wrong, it's just some random personal predictions.