There is no need to run Traefik if you already have a working reverse proxy. Also, unless your nginx is running on non-standard ports, the ports 80 and 443 should not be available for traefik, which will prevent it from working correctly.
You can narrow it down: attach to the container, this'll give you a life "feed" of all messages the container produces. Then with that running, open your app and see if the container has anything to say about the sync process.
Not for a Synology, but I doubt Hetzner cares where the data comes from. Works well, especially once you got the keys in place. Have stored and restored, it's a simple file storage.
This has little to do with the Fediverse itself and mostly with the people involved. It would be the same on any other platform, so simply switching the software stack or whatever would do exactly zilch.
A fraction of people are going to be assholes. Sad but inevitable.
and is there anything we can do about it?
You can ban the dickheads, but that'll only get you so far.
Let's Encrypt is fully automated and will issue certificates as long as you provide an email address AND have a proper, working config. Don't get stuck on that email "issue", your problems will lie somewhere else.
As always when problems arise: check the log files.
Russians, Chinese, anything from the middle east that's not Israel... Anyone except the US basically.