This film could easily have ended with Mario saying "Boy, I need a holiday after all that!" and Peach replying "I think I know just the place...".
It could then have cut to them enjoying cocktails in Delphino Plaza with that theme music playing.
The fact that they don't have anything like that in this film is pretty much why it fails for the long time Mario fan...
I never liked Mario Sunshine when it originally came out in 2002. I thought the "Mario becomes an environmentalist and spends the whole game cleaning up dirt" premise was lame.
Looking back in hindsight, it actually IS a really good game and was ahead of its time, but its still nowhere near as iconic as the other "major" entries in the Super Mario series. One that's really unrated for me is Super Mario Land 2 (it introduced Wario, for crying out loud!). It was BY FAR the best "portable exclusive" Mario game. But there were ZERO references to Supe Mario Land 2 in the new film.
In any case, there ARE a handful of references to Super Mario Sunshine, but its "blink and you'll miss it" stuff. Notable examples being the "Sunshine Travel Agency" in Brooklyn having the exact same type font as the Super Mario Sunshine logo, and Dolphin Island being alluded to.
Super Mario 64, Super Mario Galaxy, and Super Mario Odyssey were the most successful 3D Mario games, so they got most of the references.