After restoring all project files, things were still messed up. So I completely purged any Developer or Xcode folder found in /System/Library, ~/Library, etc. Then, restored from a backup. Chose June 1st which was back when I had Xcode 13.4. Also re-restored all projects (archiving off any source file changes though).
Re-installed Xcode 13.4.1 and so far things are working as expected. So between messing up my project files, Xcode 14 must have also messed up something in ~/Library, or elsewhere.
And hurray! The hot key Shift Command A in the simulator is once again toggling dark mode. I didn't mention that ealier, but that was another function I had lost. Executing the hot key briefly flashed the Features menu in the Simulator, but the appearance didn't change. Workaround was to go into Preferences | Developer, but that got annoying.