I spoke to tech support and they were insistent that 10.15.7 didn't even exist, so I guess it must be a problem with that. It's the only thing that's different to last week when it was all working fine. I think possibly a roll-back is in order.
Thankfully Lightroom and Photoshop are still working fine, I just can't install anything new/access Creative Cloud app.
Just ran into this. Catalina (64 bit) won't uninstall properly the (32 bit). I ended up trashing the applications - but eventually figured out that there were old Adobe patch files in my Applications folder that needed to be trashed, too.