At the moment my internal card reader works again. I have no idea why. I did not try anything. Just plugged in for the first time since 6 weeks or so. And now it magically works.
This is the dmesg output. Errors are gone
[ 8959.682988] mmc0: new SD card at address 0002
[ 8959.745455] mmcblk0: mmc0:0002 SD1GB 958 MiB
[ 8959.745592] mmcblk0: p1