See Spellbook's Page.

Name feels awkward. How about "Worshipful Flautists" or "Flautist Worshippers"?

Mechanic is also very awkward, but I assume that's deliberate...

I was going for a specific type I music, but I couldn't remember the name of the style. The name would be Flautists.

The mechanic comes trying to see what I'd be able to do if a card's color was important for a block. Oddly two of the three mechanics I've designed for that block are sitting in Cards With No Home.

This would feel a lot tighter if that last line was just an unconditional "Blue creatures you control have prowess"

As it is, it feels like you've kinda thrown an extra step in there, and made the wording more fiddly than needed:

As long as you have more cards in your hand than each opponent creatures you control have prowess. Oh, and ~ is blue now, for some reason.

Yes, not caring about the card changing colors would be lighter on the text. As I stated however, the color identity of cards would be a theme of the block where this would appear. The block could contain cards like Object and Myth of the Hidden Lagoon.

Basically, this is a green creature that does a blue thing. In order to that blue thing, the creature has to become blue, and it would become blue in a way that feels primarily blue.

This is an alternate way to have a creature gain color, checking for a condition rather than a cost as Myth of the Hidden Lagoon was. The two could probably coexist, though abilities that check conditions like these satyrs would probably be much smaller in number than corrupted, so that the things they check feel more unique.

The identity still works with my first example - it's always granting blue creatures something; and it can itself become blue under a condition.

Dunno, I just feel this is a bit too fiddly for the amount you're gaining.