I played through the first few levels of this and enjoyed it, although once the rules started getting more complex (which for me was somewhere around level 5 iirc) I found myself wishing a bit that it would save progress between sessions so that I could peck away at a puzzle for a bit and then come back to it later without having to keep a tab open for it.
it's also interesting to me that clearly not all the rules are self-inverse in the sense that clicking the same square twice will cancel itself out. you seem confident that the game cannot get itself into a state where an actual reset is required, so I take that to mean that each move *can* be reversed by some other sequence of moves, but I find myself wondering how you guarantee that.
(also, there's a part of me that wants both the all-white and the all-black states to be win states, given that you're always starting with a non-monochromatic state anyway, but perhaps for some rules it's much easier to get to one than it is to the other, especially given the asymmetry mentioned above.)
I doubt that I will complete this, but it's definitely an interesting and thought-provoking game to play around with!