⌘` (command-backtick) "Move focus to next window" not working on Mac Monterey

The standard Mac “Move focus to next window” shortcut isn’t working for me, even tho it works fine in Chrome, and every other app I’ve tested. I checked the Brave shortcuts and I don’t see anything that could be hijacking it. Indeed, even if I change the OS-level shortcut, it still doesn’t work. It’s as if Brave is somehow blocking OS-level window management.