How do you actually get support from Adobe?

You'll get support for making the app work - not so much for specific ways that you might want to use it. A bit like you can take the car back to the dealer if the power steering doesn't work, but don't expect them to tell you how to use the steering wheel. Here they can quite reasonably say "so what?" if you can't find pictures which aren't in an album. Sure, I can imagine why any organized person might want to do so, but it's not really a fundamental feature, is it?

"What is the recommended approach to sorting pictures into folders given missing functionality so you can't filter to determine what photos have not been allocated to a folder?"

If you want an answer, my first suggestion would be use terms more precisely - you seem to use "folders" for what LRCC calls "albums". LRCC uses "folders" for its mechanism to group albums. But assuming I have guessed what you want to do, there is no recommended approach. If you want to find which photos haven't been allocated to an (or do you mean any?) album, you can select multiple albums using the standard Ctrl/Cmd and Shift  modifiers. So select all the albums at once, then select all the visible images. Now go to All Photos - the unselected images are those not in any album. Maybe I am wrong but as LRCC lacks an Invert Selection command, I can't see any way (other than eyeballing) to select them. You are running up against LRCC's limited capabilities!