Time in GMT or Missing Time Zones in systemsetup

I didn’t have to “fix anything” so this isn’t super satisfying as an answer, but the problem has resolved itself. I see no updates that would have affected this and took no further action.

I waited about a week, but the issue persisted. I began to have issues with Calendar.app wherein some events were reported correctly (but in GMT) and some events were reported incorrectly (as if my timezone was restored to Eastern Time).

My most recent tz folder was 2021a.1.0:

# ls -rt /private/var/db/timezone/tz/ | tail -n 1
2021a.1.0

My next most recent tz folder was:

# ls -rt /private/var/db/timezone/tz/ | tail -n 2 | head -n 1
2020f.1.0

Following @armiller's suggestion, I was able to fix my Mac by running this in Terminal.app:

broken=$(ls -rt /private/var/db/timezone/tz/ | tail -n 1)
previous=$(ls -rt /private/var/db/timezone/tz/ | tail -n 2 | head -n 1)

cd /private/var/db/timezone/tz

sudo mv $broken/icutz/icutz44l.dat $broken/icutz/icutz44l.dat.bak
sudo cp $previous/icutz/icutz44l.dat $broken/icutz/icutz44l.dat

I then opened the Timezone selector in System Preferences. Now the timezone is set to a real value. My Calendar uses the correct time. Unfortunately, the clock in the menu bar was still wrong. Restarting the OS fixed the clock in the menu bar.