Here’s how I would categorize them…

Poppin Heart: Lovely

Miracle Moon: Cool

Scarlet Butterfly: Celeb or Premium

Rosession: Cool

Flower March: Natural

Bear Bear Bear: Lovely

Rainbow Candy: Pop

Love My Music: Cool

Cutie Carat: Multi type

Princess Ring: Premium

Crystal Verse: Premium/Multi type

Prism Stone: Multi Type

So Future School debuted, and I'd say Cool/Lovely(?)/Multi-Type.