It's a tricky one, we strip the bucket name from the sub-domain, because some S3 providers provide the endpoint on their dashboard with the bucket name included and if we haven't stripped the bucket name, the resulting endpoint in such format: "backup.backup.mymte.de" wouldn't actually work in that case.
Unfortunately you've discovered legitimate case where this doesn't work as expected on your end. We probably won't remove the stripping logic as I am sure that other users would complain.
The option is to rebuild the S3 screen, perhaps implement "provider dropdown", so each provider would have some custom additions to make using S3Drive easier.
I am going to create a roadmap item for that.
I am not sure if there is any easier approach to address this issue. (edited)
It is a rare case