Sometimes when the OS is updated conflicts can happen. iMovie does run on Monterey, so I don't think that you need to reinstall Catalina. It is mostly likely something involved with your setup. Here are some things that you can try.
To shake out any conflict that might exist, try shutting down and booting up in Safe Mode and, after everything loads, immediately shut down and reboot in normal mode. Now see if iMovie will launch.
This link contains instructions on how to start up in Safe Mode:
Start up your Mac in safe mode - Apple Support
If you are running an intel Mac, versus an M1 silicon chip Mac, you could also try resetting the System Management Controller. Here's a link for instructions:
Reset the SMC of your Mac - Apple Support
Another thing you can try is deleting preferences. 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. Possibly you may need to reboot to set the changes. Deleting preferences is a safe procedure that will not cause data loss or disruption to your project.
Another diagnostic tool is to open iMovie in a new library. Open iMovie while holding down the Option key and select a new or different library from the box that appears.
To rule out that the issue is caused by some conflict in your normal user account, try opening iMovie in a new or different user account. You can use the Guest account on your Mac for this purpose.
-- Rich
-- Rich