Hi once again.
Well, I seem to have found how to do it in Windows 11, to get it to work as I had in Windows 10. It is really not so obvious. So I think I now have things as they were.
For the benefit of anyone else in the same situation, what I just did now is to go the the Language settings, where I have both English and Danish installed, with English on top to be the preferred language (so that I have my Windows menus and all apps in English). From the English selection, I found out just now that I could go into the keyboard setup specific for the English language selection, and here I could select additional keyboard layouts to be associated with the English language selection. This is what I had in Windows 10 but could not until now find the way to set it up in Windows 11..
So now I have both English and Danish keyboard associated with the English language, and I have only the Danish keyboard associated with the Danish language. Maybe I don't even need the latter anymore. And I think this will now let me keep the language as English but the keyboard as Danish.
Thanks again for the help, and prodding me to keep looking for the solution!