Let us know the following
If ping works for: localhost, your gateway, 1.1.1.1, google.com.
The contents of your /etc/resolve.conf
If you have a tun0 interface (ifconfig or ip a)
You said you uninstalled tailscale. Are there any running process or active systemd units laying around?
Good that it's working (kinda).
So it sounds like your DNS resolver is botched. Id dig into the doc on how systemd-resolverd should look and see if you can't rectify what went wrong (the arch wiki should have examples of what a default config looks like).
I don't remember if arch uses cloud init configs but it being reset at boot feels like a cloud init config problem.