Is it possible to convert iMovie 11 library back to iMovie 10?

The latest iMovie version is iMovie 10.3.5. There is no "iMovie 11". The discontinued iMovie 9 was sometimes called iMovie '11 (with an apostrophe) to indicate the year, not the version. In any event, iMovie 9 would not operate on either Catalina or Monterey, and could not open an iMovie 10 library. Could you provide further details as to what exactly you did?

It appears that when you opened your Catalina iMovie library (on an external drive) with your Monterey computer's iMovie version (a newer version than on your Catalina Mac) that the library got updated to a newer library version. That would explain why iMovie can no longer open it on your Catalina computer that is running the older iMovie 10 version.

If the above is what you did, once you update an iMovie library you cannot revert back to the older library unless you use a Time Machine backup to revert to the older library version. You could revert back to it, saving it in a different location than the newer library on your external drive, so that you have both libraries -- one for Catalina and one for your Monterey Mac.

You might want to contact Apple Support and talk to the techs there. They have the capability of remotely accessing your computer, that we do not have on this forum.

-- Rich