Someone in our local Tesla Facebook group had this issue a couple of weeks ago; Supercharging worked fine but Level 2 charging at home suddenly didn't. She asked in the group if she could come by someone's house to test her car with another wall connectors. Turns out we were closest and she came to our place. Our wall connector didn't work for her car either, unfortunately. She posted a follow-up a few days later, after a visit to Tesla service, and turns out it was a Power Conversion System (PCS) issue. Not sure if she's had it repaired yet.
As you probably know, the Wall Connector and other home "chargers" aren't actually chargers, but merely supply AC current to the car, which converts it to DC and uses its own on-board charger to charge the battery. Conversely, when you Supercharge, that's DC to DC, and thus the Supercharger does actually serve as the charger and bypasses the car's own on-board charger. This likely explains why you're able to Supercharge but not charge at home.