I had a ton of fun with this, I ended up beating all 16 levels :)
My main piece of feedback is that it was very unclear how the game worked at the beginning. It took me about 5 minutes to get fully oriented.
But once I knew what was happening I had a great time doing all the puzzles. It felt very satisfying to figure out different strategies. Most of my routing ended up focusing on bringing the blue and red paths towards each other, knowing that the paths had to merge before the innermost ring with 1 exit.
I would love to see this expanded with more puzzles! Many of the later levels had a ring in the middle with just one exit, so by then you've combined paths and it's very easy to make it to the outside from there.
Overall really good work! This is one of my new favorites!