Help with iMovie after upgrading to Catalina from Sierra OS on my IMac desktop

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View your purchase history for the App Store and other Apple media services - Apple Support

That's odd. Apple usually allows existing app users to update to the newest supported version even if the latest version doesn't run on your OS. Just tested this with a Ventura 13.0 install and was able to upgrade from iMovie 10.3.4 to 10.3.8 (The current version, 10.4, requires Ventura 13.5+). The again, Apple's web page currently claims 11.5.1+ compatibility. I had thought that was outdated information, but maybe Apple has a cutoff for updating old version?

For reference: you may need to drag iMovie to the trash (Don't empty!) before you can be prompted to redownload the app (and be offered the newest supported version). If this doesn't work drag iMovie back out of the trash to the applications folder it came from.

First issue, did you say -nothing- was showing up under purchases? iMovie or otherwise? Have you ever downloaded software/updates through the AppStore other than the Catalina upgrade that you would expect to see? You may need to contact Apple Support. If you can't download or update apps on your Mac - Apple Support

Second issue, you say iMovie does not run on Catalina? Which version of iMovie? I can understand an old version having bugs/compatibility issues but I would expect anything current on Sierra would at least try to run on Catalina. (On the other hand if your iMovie originally came from an old iLife DVD package then yah... that won't run).

Just for reference: can you right-click on iMovie in the Applications Folder, click "Get Info", and check the listed version number? Just For Science to let the rest of us know what doesn't work.

Regardless I would not recommend staying on Catalina. If you need iMovie I would suggest rolling back to Sierra (assuming you have a packup) and instead upgrading only as far as Mojave and seeing if your iMovie will work there. Alternatively you could upgrade again to go further forward to Monterey (the newest OS that supports Late 2015 hardware) and then try to find a 3rd party iMovie alternative.

Note: the newer versions of MacOS really want to run on an SSD, so if you have an HDD or Fusion drive and wish to go forward to Monterey you might need to consider purchasing an external USB SSD and reinstalling MacOS onto that.

No, Catalina is absolutely fine and no, the “rest of us” don’t need “Get Info”, for “science” or for whatever. There’s no mystery to this - iMovie 10.2.5 will download if it’s there in purchases, otherwise it’s history. I think this discussion is sort of over…

It can't be done unfortunately - iMovie requires macOS Ventura which in turn requires iMac 2017 or later.

No cut-off date, 10.2.5 will download if it’s there under purchase history. Contacting Apple Support isn’t a good idea, OP’s Mac and OS are both officially obsolete.