Thanks for the answer evamvid and for resurfacing this thread. Now that I’ve also completed my (external) Thesis, I will also share my experience.
I wrote my Master’s Thesis at DLR Stuttgart and STFS acted as the supervising institute from the university side. As expected, DLR advised against making the report public. After a bit of back and forth, I managed to convince them that TUbama is primarily an archiving platform and the report would be only accessible to the examiner. Surprisingly, I did not receive any kind of pushback from either DLR or STFS and I must say that the process went mostly smooth.
Hope this helps anyone seeking an external Thesis, make sure to quote APB § 23 (8) while explaining the situation to your employer.