Thinking what I might have changed was my starting point, and as at first only firefox was affected starting in safe mode was the first step tried.
But having got the feedback from #SUSE IRC channel that many all users there who checked for me have been the same error, it’s pretty obvious that this is not an issue on my side, or? Also, as written, all my firefoxes, Linux, Android, and also on an iPhone, all called “firefox” but pretty different pieces of software, have this error. Three “corrupted profiles” etc., at once, and only for ONE website??
Guess not, but nevertheless thank you for trying to help.
P.S.: Just to mention: It works now again on all three devices without having changed anything on all of them, no firefox update etc.