Reporting from July and sadly this has still not been fixed. I need to know if the game center is open as I am doing a custom Metal rendering in my engine and want to disable rendering certain UI once the game center is open.

I fully agree. Having support for AppClips in visionOS would be a game-changer. The ability to tease the first levels of my app, an immersive and exclusive Vision Pro game, would be the perfect marketing instrument to increase awareness and drive growth.