I landed on something similar for my own game, though it's been pretty tricky.

I'm building a physics-based 2d game involving slingshotting around planets. The realtime nature of it has meant that it's nearly impossible for the AI to test using a browser mcp. It'll take one screenshot, then another, and in the intervening time the player shot off the map and into deep space.

Instead I gave it both a code-level api to step forward and backward the physics engine and a browser-based, `window.game` api to do it via a browser mcp console. The former helps it work out physics bugs and the latter helps it test animation and UI issues.

It's still not great. I keep occasionally getting "I tested it and it works perfectly!" as I stare at the mcp'd browser with the player stuck clipped halfway into a planet. I think, if anything, I need to lean harder into this approach: building really solid tooling for the AI to inspect every aspect of state. I would kill for a turn-based game like OP XD