If it's billed as a general Direct, there will absolutely be at least one new first party game announcement, and probably two or three. To my knowledge, Nintendo has never had a general Direct in the Switch era without announcing at least one new first party game, and usually they open and close with new first party announcements and often have a third lesser announcement near the middle of the presentation, though a few times they've opened with DLC or a big third party announcement (like Monster Hunter).
Honestly, I'm prepared to be pleasantly surprised, but the BeatEmUps leak reeks of bullshit to me. He also has no track record, so I'm going to be skeptical until he gives me a reason to trust him. Could be biased here though, because I find him deeply obnoxious and have no idea how he's built up such a huge audience.
I'd also put the chances of a 3D Mario announcement at much greater than 0% if they really did hold the Direct until after DKB released. I know people are expecting it to be announced during a Mario 40th anniversary Direct in September and that's totally plausible, but waiting for DKB to release makes me think the Direct is going to feature a game that would have competed directly with Donkey Kong and Animal Crossing appeals to a very different audience. 3D Mario is the only game that fits.
That said, Nintendo may have waited for a different reason. Maybe they really are just trying to do distinct "waves" of Switch 2 publicity, or maybe there's no July general Direct and we're going to keep getting Nintendo Today drops and game-specific Directs until September. If this leak is correct though, and DKB really is a key factor in Nintendo's timing, I think 3D Mario is probably the underlying reason.