Time in GMT or Missing Time Zones in systemsetup

The problem

MacBook Pro (Catalina 10.15.7) decided to start showing GMT in the status bar and system preferences last week. It is physically in Pacific time (PST) and I'd like it to show that time instead.

Troubleshooting thus far

Following Apple instructions

• System Preferences > Date & Time:
  • "Set date and time automatically" is turned on using Apple Americas/U.S. (time.apple.com.) (problem persists with all servers)
  • "Set time zone automatically using current location` is turned on
  • Time Zone correctly locates me in PST
  • Time Zone listing is empty
  • Privacy settings are turned on to allow location services for Time Zone & System Customizations
• Computer has been restarted several times
• PRAM has been reset several times
• Computer is connected to wifi

Following this post:

• localtime is correct as are link to database and permissions
• Accessibility has been reset
• ntpdate has been run

Current situation

(Really, more of "The Problem" but with a lot of the basic troubleshooting out of the way. Maybe this is "where it gets good".)

• date returns the correct (local) time
• systemsetup gettimezone returns GMT
• systemsetup listtimezones returns Time Zones: and nothing else
• systemsetup settimezone America/Los_Angeles returns America/Los_Angeles is not a valid timezone

Did the timezone list somehow go missing? Can I add it manually? Is there an update I can run to re-link this somehow?

I'd like to resolve this without an OS re-install if I can. Help me Ask Different, you're my only hope.