The SD card is actually a very simple replacement. A few screws and the back plate comes off, then the card reader is a separate board. Ifixit places it at a 10 minute fix. No soldering, no replacing thermal paste. Assuming it’s just the reader and not something in the software, $20 and it’s fixed.
https://www.ifixit.com/Guide/Nintendo+Switch+Micro+SD+Card+Reader+Replacement/113031