I highly recommend using
TinWoo Installer instead. Its what I personally use and I never had any issues while using it.
- emuMMC isn't designed to provide protection; its just a copy of your sysMMC on an SD card. However if one were to use CFW & homebrew exclusively in emuMMC but never go online, sysMMC will remain untouched and Nintendo will not notice
- emuMMC is designed to run higher firmware versions without updating the actual firmware of your console. Outside of that, it can act as a brick shield
- You don't need to make the partition as big as possible since you can just install games to the SD card
- Read the second bullet point
- There is a limit to how far games can be dowgraded which is determined by the SDK they were built with. Suffice to say that this will not work forever and you will need to update to play newer games.
Is it partition or file based emuMMC?
https://gbatemp.net/threads/running-atmosphere-on-patched-sx-core-switch.574083/
That is because Tesla doesn't support firmware 13.1. This is also why you should never be in a rush to update because CFW/homebrew actually work worse on higher firmware versions.
Unfortunately, this sounds like your SD card reader might be broken/faulty. This is a hardware issue so aside from replacing or trying to fix the SD card reader, there isn't much you can do.