Thinking out loud here, but you could make an application that's always running, always has screen sharing permissions, then exposes a lightweight HTTP endpoint on 127.0.0.1 that when read from, gives the latest frame to your agent as a PNG file.
Edit: Hmm, not sure that'd be sufficient, since you'd want to click-around as well.
Maybe a full-on macOS accessibility MCP server? Somebody should build that!