Oh this is strange... now it running properly. Today I restarted my machine again (was running via suspend only for the last days). There was a kernel update a week or maybe two weeks ago, so it is possible that this was my first restart after installing the update. Now with kernel 5.3.18-59.24, I get the proper mmc0 messages in dmesg, and KDE also detects the SD card properly. BTW: All the kernel sub packages were installed, even in the old kernel version. If you are still interested in the output of dmesg and hwinfo, I can attached it.