Just renaming the file didn’t work. I copied the photo for the background to all directories I could think of (/images, /template/images, /css, /template/css). Now the background is there. I just have to figure which one was the appropriate directory. Or the syntax of the path in the css file.
For ages I tried to connect a domain to a webspace. I did that before, but couldn’t remember how I had done that. My webspace is at ionos (before 1und1). I think I figured that as well: I had to click on “Connect domain using domain connect”. Then after one hour (possibly up to 48 hours) the domain was connected. Works even with subdomains.