I'm not entirely sure if iMovie '11 will work again afterwards and I have only used iMovie from the App Store but you can try... You can create a Time Machine backup or any full system backup just in case a function or feature in iMovie '11 is no longer available in the newer version... Create a backup first before attempting to do that...
However, if you are okay with replacing iMovie '11 with the version from the App Store and don't have any function or feature that you might miss with switching to the newer version, then go ahead... I have never used iMovie '11 so I can't compare the features with the newer one...
Or you can keep your current setup, import and export the screen recording using QuickTime then attempt again to edit in iMovie '11 or use another video conversion software or just use a different video editor entirely...
You can also seek help from an Apple Genius by visiting your nearest Apple Store or contact Apple Support over the phone... Or just check first what others say about your situation...
Much prefer a newer iMovie regardless. I just assumed if I can ever get the later version of iMovie from the App Store, it has to be an improvement on the one I use, which is not the best, mainly because it whites so much out, and despite playing around with colour and contrast, it's never the same as the source material. Always look a bit lousy compared to source.
Have you ever signed in with an Apple ID on the App Store or iCloud on the MacBook Pro?
A different Apple ID might have been associated with iMovie '11 or the MBP in general which could have led to that error message on your screenshot from before...
I've used the same Apple ID on my phone and MBP since I ever bought Apple stuff, 15 or 16 years ago, which still works fine if I download from iOS store, and never had a problem, I only get that message on High Sierra when trying to update in App Store, using same ID. Even iTunes accepts it no problem on same MBP. It's just this. There's no good reason why it should say that, but I don't think I'm alone with that problem. Not that I saw resolution for it with others.
Will try backing up all over weekend and give another go. It's mightily frustrating it can't just update it whenever I open iMovie and it tells me to update it.
Thanks again!