Hi,
That is happening because iMovie is opening in a library other than the one in which you created your projects.
Go to your external drive where you moved your libraries and double click on the icon of the iMovie library in which you want iMovie to open. This would be the one in which you created your projects. iMovie will open in that library and your projects should be available. The next time you open iMovie it will open in that same library as well.
Before moving an iMovie library to another drive you should do a File/Consolidate Library Media to be sure that the library takes with it all media used in the project. Usually you will get a message that there is no media to be consolidated.
The external SSD should be formatted Mac OS Extended (Journaled) or APFS in order to store an iMovie library. If you have to reformat the drive, be aware that reformatting deletes all data in the drive. So before reformatting be sure to back up elsewhere any data, such as the iMovie library you moved there.
-- Rich