If the time is off by that much after being powered off, this tells me two things:

1. Your RTC battery is very likely dead. Should be simple to replace, it would be on the motherboard but then again accessing it might be a little tricky on a laptop
2. NTP is probably not set up, or set up incorrectly. It should automatically sync the time on boot

An incorrect clock can absolutely cause network issues, so I would bet that’s what is causing you trouble

Why are you using networkd instead of networkmanager on a desktop?

What a weird question. Networkd works anywhere systemd works, why whould desktops be any different.

It’s the same as asking someone “why are you using systemd-boot instead of grub?” Because I like systemd boot better and it’s easier to configure. Same with networkd, configuration is stupid simple, I have installed it on my work machine even.

As for op: since you can manually ping ip addresses and the issue seems to be time-based, could it be that your machine is somehow not renegotiating a dhcp lease?

That’s not enough, a better idea is to, somehow, poison the location data. Otherwise by disabling location tracking you still leak the information that you are going to a clinic.