"If you need to use Esc to force an app to close, you can switch to another app and try Option-Command-Escape. You can also choose Apple menu > Force Quit."
https://support.apple.com/en-ca/HT207358
In the video linked above the Apple menu also didn't appear to work, despite the mouse cursor moving, which matches my experiences.
Exactly - what not everyone realizes is that the top menu is rendered and events from it are dispatched into the process of the current (active) application. If that thing refuses to return from an event handler dispatched from the main thread's run loop, (i.e. most cases where program has hung), you can't use the Apple menu.