Hi,
In your case, not sure what is going on there. iMovie seems to be struck. When iMovie is taking too long to complete other tasks before closing, I've just force quit with no consequences. If you are worried, just make a copy of the iMovie app as a backup and then force quit the original one. In any event, the projects are stored in the iMovie library rather than the app itself. For example, you can completely delete the iMovie app (not the iMovie library) and reinstall a new one, and the new one will access the projects from the existing iMovie library.
If the force quit doesn't work, you can always go to the iMovie backups folder to retrieve a previous backup of your iMovie library, and open your projects from there.
To get to the iMovie Backups folder, follow this file path from the Finder menu:
Go/Home/Library/Containers/com.apple.iMovieApp/Data/Library/Caches/iMovieBackups
NOTE: If running Ventura or later, in the above file path substitute iMovie for com.apple.iMovieApp. So, for Ventura, the file path would read:
Go/Home/Library/Containers/iMovie/Data/Library/Caches/iMovieBackups
When you get there you will see a list of previous backups of your iMovie library. Click on one dated just before your issue started. iMovie will open in that library. Navigate to your projects browser (where your projects are displayed as icons) and see if your projects are intact.
Alternatively, you can use your Time Machine backup to restore your library to a point in time preceding the issue that you are experiencing. You would lose any work that was done after the date of the Time Machine backup.
-- Rich