How do I fix the error code "2101-0001"

Repair.wiki has a page on this specific error, and it appears to be related to the charging port itself. Their main suggested fix for it is to unsolder the USB-C connector and replace it. That could certainly explain your Switch's failure to be able to charge in the first place. Here's a link to their page.

Nintendo Switch Error Code: 2101-0001 - Repair Wiki

Here's what they have to say about possible causes of this error.

This error code is generally caused by M92T36, the power management IC for the Switch. 2101-0001 is an error on the i2c bus. This is a faulty M92 in MOST cases. There are cases where it can be something such as a faulty charging cable, excessive force, or accidental damage when inserting and removing the charging cable. It is not usually an error that will just occur on its own for no reason. Because this is a hardware-related (critical) error code, replacing components is your only option.

This error code is generally caused by M92T36. 2101-0001 is an error on the i2c bus.

This error code can be caused by the user inserting the cable incorrectly (on a strange angle).

This error code can be caused by faulty accessories, such as a damaged charging cable or dock.

This error code can be caused by some poorly created 3rd party USB-C accessories which lack proper circuit protection.

Obviously you'll want to start with eliminating other components as the cause first before going through the difficult process of replacing the charging port. Try a different charging cable and a different charger first. Clean out the port with a toothpick or other non-metallic object and isopropyl alcohol (90% or higher concentration).

Replacing the port itself is not an easy job; I consider myself a pretty experienced DIY-er with decent soldering skills, but I'd hesitate to have a go at that repair myself. Should be straight-forward for a repair shop and shouldn't cost too much if you've got someone local that can handle it.