The vast majority of SmartThings processing is not on your Hub, and much of that will actually run independent of a Hub.
You can actually create a Hub-less Location (in the IDE) and, I think, drop some Virtual or Simulated Switches, and/or other Virtual / Simulated devices in it.
All of these will do at least some minimal amount of debug Live Logging. To be sure, you could even create a simple DTH or SmartApp (from template code) and be certain to put in log.debug, log.error, etc. commands in places which will definitely execute (e.g., installed()).
The simulator in the code editor also will write immediately to Live Logging.
In other words … you can do a lot of exploring & fiddling that would “obviously” force logging … just to see if something or anything manages to show up in the Live Logging.
If nothing logs, then my recommendation remains to consider wiping your entire Account (i.e., exclude all your Things, and delete your Location, have SmartThings delete your Account, and start fresh with a brand new email address or email alias (firstname.lastname@example.org). You may need support to reset your Welcome Code so that you can join your physical Hub to that new Account.