I recently upgraded to ios Monterey. Several functions in iMovie no longer work as they did before.

I don't run Monterey, so can't look for myself. You didn't describe in what way that the iMovie functions were different or whether they were intended differences or malfunctions.

However, if you haven't already done so update iMovie to current version.

Then do a delete preferences procedure. To delete preferences open iMovie while holding down the Option and Command keys and select to delete preferences in the box that appears. iMovie will open in a new library. Reopen your old library to get back to your projects.  Deleting preferences is a safe procedure that will not cause data loss or disruption to your project.

-- Rich