How does the time synchronization work in PureOS?

I don’t know. It’s still not working the way I would expect. It is still working the way the documentation suggests that it can under certain assumptions that various things aren’t working properly (since there are multiple fallbacks to maintain the correct time before reverting to a build date).

It was confirmed here that the Librem Mini v2 has an RTC with button cell.

Do you want to open yours up and see whether you can see a button cell? I would carefully extract the battery and check the orientation (polarity) of the battery. If you have a multimeter, I would also check the voltage on the battery.