What a cool and unique idea!
I love all the different directions you tried taking it in too: resource management, a painting tool, and a rhythm game.
But ultimately I was really wow'ed by your concept of maximizing your connections while minimizing your footprint, so to speak. It naturally lead to some really organic structures, which was really cool to see.
I played around with cellular automata that had similar rules (on a grid), and it was one of my favorite generative projects simply because of how strangely natural it looks, so I KNOW you have something here that could be fascinating.
Here's a suggestion: with every turn, the oldest parts of the roots could become rigid, so the player cannot build upon them. That way, the player has to carefully build up the root's foundations (but not too much!) before moving closer to the next nutrient/goal. It's a balance between structure and progress.
TBH I really enjoyed the challenge of the rhythm game, the sudden increase in energy was exciting haha - I love when moody stuff gets funky haha! It just is funny how it throws you into it out of nowhere.
Lot of cool ideas here, a love jam entry!