Fortunately/unfortunately, I’m one of those few that uses Systemd. And lucky for me I found a fix this evening!
systemctl status dbus
This output only one failure which was for the ModemManager which I believe I can safely ignore since I am on a desktop PC which does not have a 3G/4G modem in it.
Anyway, what ended up working was after the “list-timezones” command didn’t work I decided to dive deeper into /usr/share/zoneinfo, and it was here that I found the files which configure the various timezones.
Interestingly enouigh after catting out a few of the files in this directory I found quite a few of them were empty. Which I checked my timezone and it was empty, but UTC was not. So at this point I decided to remove tzdata (cached version too) and reinstalled it via Pacman.
sudo pacman -Scc
sudo pacman -Rsn tzdata
sudo pacman -S tzdata
Which at first “sudo timedatectl list-timezones” still produced an error, so I then checked to see if there was perhaps a service that needed to be running, so I found there was “systemd-timedated.service” and "systemd-timesyncd.service " available, which I saw timesyncd was running, and timedated was not. So I attempted to restart timesyncd and then enable/start timedated.
sudo systemctl status systemd-timesyncd.service
sudo systemctl restart systemd-timesyncd.service
sudo systemctl status systemd-timedated.service
sudo systemctl enable systemd-timedated.service
sudo systemctl start systemd-timedated.service
I received an error about timedated.service not needing to be enabled as it is usually called on by another service (timesyncd?), so it shouldn’t be enabled via systemctl, but for whatever reason I ignored that and attempted to run “sudo timedatectl list-timezones” again. This time it output a long list of all of the timezones that were re-populated under /usr/share/zoneinfo by pacman.
❯ sudo timedatectl list-timezones
Africa/Abidjan
Africa/Accra
Africa/Addis_Ababa
...
I was able to verify everything was okay with timedatectl again by using these status commands:
After that bit of success I decided to try running:
sudo timedatectl set-timezone America/Detroit
Which as I had mentioned in my previous post, when I did this before it would set my Calendar month to 0, and have the days set from 1-42, and the digital-clock widget would be blank.
Well, this time it did not do that! 
Which I was also able to confirm everything was working with timedatectl using the following commands:
❯ sudo timedatectl status
Local time: Fri 2024-10-04 20:23:38 EDT
Universal time: Sat 2024-10-05 00:23:38 UTC
RTC time: Sat 2024-10-05 00:23:38
Time zone: America/Detroit (EDT, -0400)
System clock synchronized: yes
NTP service: active
RTC in local TZ: no
❯ sudo timedatectl timesync-status
Server: 104.156.246.53 (2.arch.pool.ntp.org)
Poll interval: 34min 8s (min: 32s; max 34min 8s)
Leap: normal
Version: 4
Stratum: 2
Reference: CC093677
Precision: 1us (-25)
Root distance: 16.021ms (max: 5s)
Offset: -256us
Delay: 52.910ms
Jitter: 2.769ms
Packet count: 9
Frequency: +9.309ppm
And as a “bonus” I can also now change the timezone from the settings menu via the “Date & Time” section. All of the timezones now have flag icons next to their respective names, and there are comments included too which were not there previously.
So it seems the issue here was some sort of corruption of tzdata. 
Thanks @aerostar666 for replying so quickly on this old thread, I really appreciate the help!
Edit: I’d be curious to know if @Zbquhlhu is using an i9 13900k + Zen Kernel + Nvidia too?