EDIT: I am not sure tbh whether it was fixed by version 6.0.6 or whether I just entered the URL correctly for the first time since January, however, I got it running again in my internal network with the following settings:
URL: https://<internal IP of Synology>:5006/home
User + PW of my (non-admin) Syno user
Skip HTTPS certificate check
Please confirm in Synology's WebDAV settings (reachable via package manager) that HTTPS is activated and set to port 5006 (or adapt accordingly).
If you have HTTPS certificates installed, you don't have to skip the check, of course.
Please note that my vault file was always located and is still located under /home/Enpass
Finally I don't have to do the synchronization by this annoying backup workaround anymore.