Hi everyone,
I followed the guide at How to fix CalDAV|CardDAV|WebDAV problems and was able to solve the problem on my own. It turns out that there was no .htaccess file in the restore/ dir. Simply copying the old one worked, guess it enabled the header rewrite module.
Still many thanks for anyone thinkink about this problem!
I will continue working on my Backup/Restore client mentioned in the first post (Integreating more tests, supporting ssh key auth and other stuff)
Please mark this thread as solved and close it.
Best, Lukas