I also have this issue frequently in Cursor version 1.1.6, on MacOS 15.5.
Ctrl + I does nothing for me.
Also, once you try and close the chat, it does not close, but if you switch away and back again, it just says “Loading Chat” with a spinner, and never loads.
Quitting Cursor completely and reloading it results in the chat tab that we tried to close not re-appearing, so there’s a workaround.