RESOLUTION
I was able to fix the problem (by reading the Hetzner documentation 
).
This is not a TrueNAS issue, but a Hetzner problem.
So for anyone having the same issue in the future, here is the solution:
According to the Hetzner documentation, you CAN NOT use absolute paths.
So if you create a folder called “backup“ in your storage box, you CAN NOT address it with “/backup” but rather with “backup/“ (I guess this is also the reason, why the remote folder picker in TrueNAS does not work.
You have to use a relative path, so basically just omit the “/“ at the beginning.
This configuration finally worked for me:
Also, dont forget to encrypt uploaded files, as this is (to my suprise) not enabled by default.
Edit: oh yeah I forgot to mention. Since the remote folder picker does not work, you (obviously) have to manualyl type the remote path, as mentioned in my initial post.