Hi, 
I don't know why the restored iMovie library won't open.   Where is it stored?  What steps are you using to try to open it?   
In any event, you should be able to recover your iMovie project from the iMovie Backups folder. 
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 and then you should be able to open your missing project. . 
The opened backup library will not overwrite your existing library. 
-- Rich