@fliegerhermi
Most things are not strange - strange things are often the result of the wrong questions being answered or the right questions being incorrectly answered.
For instance, it can be the case that your FTP user has not been setup properly and/or that the remote backup directory has permission issues.
In this situation, I would really recommend to
1 - using an existing directory in the remote backup domain, preferably the "private" (sub-)directory (read: restricted or less accessible from the web)
2 - create a new FTP user that has the "private" (sub-)directory as "home" (landing) domain
3 - change the backup settings of one small domain in order to have backup processes use the newly created FTP user,
4 - run a full backup for that one (small) domain
5 - add an empty (test) file or a (test) file with the contents "test" to that one (small) domain
6 - run a incremental backup first,
7 - remove the test file and rerun the incremental backup : this is to check whether the incremental backup removes the test file (as it should!)
8 - create a second test file with a different name
9 - rerun a full backup and check whether the second test file is included
All of the above is basic testing, in order to determine whether the backup processes are working properly.
If the backup processes work properly, then there is - apparently - an issue with either your old FTP user setup or the old backup directory.
One can focus on the solution of the issue(s), but one is better off by simply changing to the new FTP user settings.
If the backup processes do not work properly, then there is - very likely - an issue with your FTP configuration (either remote or local) or server settings.
One can focus on the solution of FTP config / server settings related issues later ........... there probably is no need to do so.
As a final remark, whenever setting up a remote backup domain, then one should ascertain that the backup domain is not accessible from the web.
There are many elaborate solutions, but there are also some simple solutions : one can - for instance - backup to a domain that has hosting deactivated.
However, first things first, let's try to get the backup processes working without any minor or major issue!
Kind regards.....