Syncthing is one of the best software I used. I use it to sync my notes.

separate the data-directory from the appdata-directory

Would you mind explaining more about this?

No, I don’t want a second container for a database.

Unless you’re talking about using SQLite:

Isn’t the point of Docker container is to only have one software/process running? I’m sure you can use something like s6 or other lightweight supervisor, but I feel like that’s seems counterintuitive?