I have found little info on how to repair an iMovie library without triggering the prompt to do so. One poster on this forum found that he could trigger the prompt by removing a project from the library and then moving it back in. I have not tried that, so can't vouch for it.
One workaround would be to copy your projects, one at a time, from your old library to your newly created library. Then confirm that everything is working properly on your new library. That should work around any corruption that may have existed in the old library's structure.
As you mentioned, a Time Machine restore of your old library might work, if you can restore to the point before where the corruption occurred. I always worry that doing that might make your projects unreadable if you had done any iMovie updates. Also, you would lose any work that you had done in the interim time. So if you restore an old library you should not overwrite your present library, but rather restore the library to a new place or back up your present library elsewhere.
Rather than doing a restore procedure you first should try looking in the iMovie Backups folder on your Mac to open a previous backup of your library. 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 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 working properly.
Although the problem seems to be solved with your new library, you might try doing Apple Diagnostics check as well, to rule out a hardware problem. This link will describe the process:
https://support.apple.com/en-us/HT202731
-- Rich