Going through some of that, it seems to be reader and/or card error, and some say it takes multiple inserts for the device to show up properly.
Also, another common issue reported was with multiple card reader devices, and needing to black list one of those.
Did this device as expected with previous Slackware versions?
[ 7.617479] mmcblk0: mmc0:d5c3 SD02G 1.83 GiB
Is interesting, as that shows the kernel found a ~2GiB drive, and should
be in /proc/partitions?