Thanks, Luis. I called AppleCare earlier, and after quite a bit of digging, they finally figured out that I needed to first check the "Manually manage..." button under "General" to enable drag and drop. Once I had successfully copied the movie to my iPad, I unchecked that button. I remembered that this button used to be in iTunes, but in a different place.
BTW, the AppleCare rep also confirmed that the list shown in the Finder window for my iPad does indeed show media on my Mac, to be selected for syncing with my iPad, which does make more sense. This is the way it used to work in iTunes.
What remains a mystery to me are the criteria by which Catalina determines which movies, etc. on my Mac it will show in that Finder window (as selectable for syncing) and which ones it will ignore. Even after I've added this movie to my iPad and synced again, the Finder still doesn't include it in the list of syncable movies on my Mac. I wonder how media files are "blessed" by the OS for this purpose. 🤔