Nice concept, very joyfully presented :)
It’s a minor gripe- but I think you could rationalise the control scheme a bit; I was quite often surprised- like how you have to click to do the first join, but then the buds link together automatically on touching. If you carry on developing it, a scheme where you join on touch and then have a key to separate starting from the back most, I think, would be a bit more intuitive, allow you to solve all the puzzles, and avoid the mouse context switch.
But I had a lot of fun, so :D