I immediately got a lot of problems with iMovie after installing Monterey! It took so much time to try to load my library, that I thought "wrongly" that it was damaged! I put it in the trash can and emptied it in order to reinstall my library from TimeMachine. It was a disaster as my internal SSD refused to free the space from the old library and therefor I did not have enough room to reinstall it. After talking to Apple for about an hour, we have not found an other solution than erasing the whole SSD and restarting my iMac from scratch. I decided to make an 100% clean install as I was piling up the new macOS systems since 2017 on the top of each other. So, I did not import the whole thing from my spare disk, but installed Monterey clean and then It took me about the whole week to reinstall all my softwares and reset all the preferences the way it used to be. Fortunately several things like my pictures came automatically back from iCloud. Well, my iMovie is still sluggish but here is a "bad & temporary" solution:
You start iMovie in the evening. it gets indeed stuck on "Loading..." coupled with the beachball of death. The app itself is reported as "not responding". BE CAREFUL, THIS IS NOT THE CASE! IT IS JUST TAKING A VERY VERY LONG TIME TO LAOD! The next morning the library is indeed there and every thing works again. Very slow, but It works.
Hope it will help a few of you!