Hi,
One backs up an iMovie project by backing up the library that contains it. You can use a Time Machine backup or copy and paste the library's icon into an external drive that is formatted Mac OS Extended (Journaled) or APFS.
Or, you can copy the project to another library so that you have the project stored in two places. Create a new library and open both libraries and, in the projects browser of the library containing the project, move your cursor over the project to reveal a little circle with dots in it to the right of the title. Click on the circle and a dropdown menu will appear. Click on "Copy to" and select the second library. The project will then be copied to the second library and will appear in the projects browser screen of the iMovie app that is on the second library.
Or, you can share out (export) the movie to your desktop to create a movie file version of your project that you can store anywhere. You can export from an iMovie project as many times as you want.
However, iMovie automatically backs up as you do your editing. It makes automatic periodic backups of your iMovie library to 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 the most recently dated one. iMovie will open in that library. It will not overwrite your current library. Navigate to your projects browser (where your projects are displayed as icons) and see if your projects are intact.
-- Rich