So I think I figured out their unifying design theme:
>floating "props" and shit

Skele obviously has the fire bird that it gave a soul to upon evolving, then the bird becomes the microphone for its signature attack. Meow has the flower which, according to its Scarlet entry, it uses "reflective fur in its cape" to make it look like it's floating; the flower is part of its signature move. Quaquaval is hard but I think it's the tail feathers, which appear down when out of battle but then spread out into an array like a floating peacock tail. They aren't totally used in its signature move but I'd imagine they're part of its whole "theme." That's at least my best guess...