回答“My right joy-con is not being recognized as connected into the switch.”The metal connection rail on the Switch can go faulty as well as the associated rail on the joycon. I think detection is made via NFC. If a known-good joycon does not detect then replacing the rail on the Switch can solve the problem.
回答“joy cons don't charge”This fault was baffling us here at work where I repair games consoles for my employer. Just today I noticed that of all the Switch units that were charging the tablet but not the joycons, the fan was also not spinning on all of them. Two identical faults across multiple units got my spider sense tingling so I decided to disconnect the fan temporarily and, you guessed it, when I attached the joycons the joycons display status screen on the Switch showed that they were now charging. I replaced the fan and this solved the problem so it seems a fan fault is also causing the symptomatic behaviour of joycon charge failure.