Luckily, solving the problem at the server side, is just as easy as fixing it on the client side.
For me it seems, that I simply installed the server using an early ISO version. As a result Windows Defender signatures were out out date and the update failed.
So in order to fix the problem, simply open the updates settings window, then click the “Advanced options” link.
At the advanced options window, enable (tick on) the option to receive updates for other Microsoft products.
Then return to the main updates page, and retry the update process.
This time Windows defender signatures will also be updated, and the entire update process will also be successful!