No, I played around with Terminal.app for quite a while already. Actually the category does show up on another machine of mine (see edit)... I suspected that maybe I never ran Xcode on the first machine since I upgraded to Catalina, so I launched Xcode, but again, no luck. I'm at a complete loss now.

Terminal actually gives an error if you poke into the top level library folder with full disk access disabled, no prompt to change without me looking on stack overflow for the solution.