I think each stage is gonna be like a Paper Mario chapter
So each one gets a bespoke scenario, some of them more action-platformer heavy, some more puzzle focused, with the lobby of the theater the primary hub zone.
But more importantly, by staring at the image of the outside of theater that is towards the
bottom of this page of the website, I've deduced that there are still
at least two Peach occupations left to see: two posters that seem to indicate an
Ice Skater in a cold northern lights area on the left side of the theater & all the way to the right is a poster that screams Anime-style
Super Hero
There's also what looks like a Paragliding mini-game segment for Detective Peach
also just above this image on that page there is a some more footage of each stage. Definitely gives off more Paper Mario-y chapter vibes than anything Luigi's Mansion to me
My guess is either Good Feel
or Hal Labs. There's is something very Kirby about this game imo