I had a view on Joplin server some month ago. As far as I can remember in the official docker Image the data was not persistent at this time, and data got lost after an update.
Question:
For the official Joplin Server docker file, is the data safe and persistent to do updates e.g. with watchtower?
Yes, it's persistent if you use a named volume/bind mount for the database. Use the example docker-compose file to get it right. Back up your data beforehand.
Doing automatic updates with watchtower has not caused any issues so far for me. You still might want to do regular db dumps as a backup routine in case anything goes wrong.
you should probably change that in your .env file but you're right. I would put https://joplin.domain.com (with protocol) there but I'm not sure whether or not this is required.