The problem lies in the fact, that a VPN connection can only be established as a local user on a windows PC, but not as a remote user. Therefore, it is not possible to access the repository directly from the remote desktop. As Git is a client-side version control system, I can pull all files in the repository on my host PC and copy the files to the remote PC using Google Drive. When I unpack the files on the remote PC, I can now Work with them and locally interact with the version control system (commit changes and compare with other branches). After the work is finished, I need to copy it back to the local system to be able to push the changes.
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Good workaround for this issue! Might come in handy for a future exercise. There war also a in-browser VPN solution for the TU Wien VPN, but after a quick lookup I could not find it anymore, so it might be discontinued.