They are? Games need pretty much all the performance they can possibly get. Can you sandbox them without having a performance impact?

Consider that people pay a $300 premium to get ~10% better performance (buying an RTX 5080 instead of a 5070 Ti).

Personally I know that sometimes closing the web browser in the background makes my game run better - that web browser doesn't even interact with the game! Would a sandbox have a smaller impact?

It certainly could.

Buying a better GPU improves your graphics performance and that's basically unrelated to the area where a sandbox impacts performance.

Killing your web browser is probably just lowering memory pressure?

Sandboxes add overhead to syscalls. It's kind of similar to running under Wine, which also adds significant syscalls overhead. Wine also has a much more impactful DirectX translation layer, so your sandbox performance would be probably be much better than the Wine performance.

Most of the sandboxing you need for a game is less full sandbox and more a whitelist on file access and local network communication.