A compatible version of iMovie for a 2011 iMac?

As long as iMovie 10 was on your computer at one point in time, even though later deleted, you might be able to obtain the highest version of iMovie that your operating system will run. Not sure what effect that wiping the Mac would have. However, try this procedure:

To update/redownload iMovie 10, drag your iMovie 10 app from the Applications folder into the trash, but do not empty the trash. (You can skip that step if you had iMovie 10 on your computer before, but deleted it.) Sign in to the app store and open your purchases folder by clicking on your name at the bottom of the app store side bar. (NOTE: For El Capitan and older, click on the Purchases tab at the top of the app store screen and then sign in. Click on Purchases again to reveal your purchases.)  You

will see your purchases displayed, including iMovie 10. Redownload/update iMovie from there. If not successful, drag your present iMovie app out of the trash (if you moved it there) and return it to the Applications folder.

-- Rich

Yes, I realize that you will not be able to download the most current iMovie version unless you upgraded your operating system to Monterey, that you are unable to do. The procedure that I suggested may be able to let you obtain the highest version of iMovie 10 that your present operating system can run. So if you have not done so, it doesn't hurt to try the procedure.

If still no luck, take a look at this thread where the poster there who was running High Sierra was able to obtain iMovie 10.

iMovie for High Sierra 10.13.6 ???? - Apple Community

-- Rich

Rich suggested signing into the App Store and looking in your purchases.

Did you try that?

You may see iMovie listed but it may be version 9 which would have been loaded at purchase.

Are you actually running High Sierra?