Tools to test surface control mechanics by computer
I doubt this exists. The best board game implementation tools you can get currently are tabletop simulator and tabletopia and both shy far away from implementing the actual rules.

I'm currently designing a board game myself and am in multiple communities regarding board game design and no one has ever brought anything like that up. I've seen a lot of tools being mentioned, from the directly usefull like card generators or the aforementioned TTS/tabletopia to more meta things like anydice, but I've never seen someone mention a board game AI simulation tool.

The closest thing you might get is VASSAL which is a free open source game engine, but that has ZERO AI support as of now (but being open source, that could be changed by you).