Hi,
The iMovie app and its library are not part of the Mac operating system. So an update of the OS should not make your projects disappear. It appears from your screen shot that iMovie has opened in a new, essentially empty library. That can happen sometimes after upgrades. Is it possible that your old library containing your projects is located somewhere other than in your Movies folder, such as on an external drive or in your Applications folder? If so, you can close iMovie and double click on your old library's icon and iMovie will will open in that library with your prijects in it. Try looking in those places or running a spotlight search.
You said that you didn't see the backups. Not quite sure where you looked. iMovie automatically keeps a backup copy of your iMovie library in the iMovie Backups folder. To cover the bases: 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
When you get there you will see a list of previous backups of your iMovie library. Click on one dated just before your Monterey upgrade. 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.
Also, if you keep a Time Machine backup, you can restore your iMovie library to a point in time preceding your upgrade to Monterey.
Also, make sure that iMovie is updated to the highest version that Monterey can run.
If none of the above work, you might want to call Apple Support to talk to the techs there. The have the capability of remotely accessing your computer that we do not have there.
-- Rich