I had a similar issue on my Pixel 6, where I’m using Nova launcher. (I know they changed hands and are not great now, but it’s still more usable than the Pixel Launcher.) There the solution was to go into the Apps settings, find Pixel Launcher, and choose force stop, then clear cache, then clear settings. Apparently there was some bug in Android 14 causing both launchers to try to intercept the “recent apps” press, and it caused it to hang like that.
Obviously that’s not going to be exactly the same issue on your phone, since presumably Pixel Launcher isn’t on there, but maybe doing the “force stop, clear cache, clear storage” on the default launcher on your phone would help?
In addition to “format shifting,” which is a well-recognized use case, and game preservation, which is a huge and under-recognized public interest in emulator development, emulators are also used for the development of homebrew software. E.g., there’s a port of Moonlight for the Switch, which lets you play Steam games streamed from a PC using your Switch, letting it serve many of the purposes of a Steam Deck. That’s huge! It would be way less practical to develop this kind of software if you could only test on real hardware. Testing on real hardware is also essential, of course, but testing on an emulator is vastly faster for rapid iteration.