I don't think there's really a framework for that sort of analysis yet. Go players talk about influence and structure but they aren't thinking of a move shrinking the problem space in that way, even though of course it does.

And mathematical analysis has so far mostly (afaik) been about the broader game. Trying to use computation to understand the value of individual moves in this way is pretty much exactly the dead end that caused deepmind to wind up using the approach they did. An approach that certainly wins games, but so far it has been up to normal go players to explain why, and they use traditional go player tools to do so.

If you find anything let me know bc it's super interesting. But I think what you're looking for is an as-yet-unwritten math or CS thesis written by a serious go playing phd candidate.