Why are my AirPods Max disabled when charging?

I just purchased AirPods Max on eBay. They were listed as “like new” condition, but didn’t arrive quite that way. The Digital Crown works, but has a rough, crunchy feel like there’s some dirt in there. Haven’t had time to use the air compressor and see if it’s something that can just be blown out. Luckily the seller refunded half the purchase price for this reason. So I still feel I got a decent deal.

Anyway to the point, the other big issue is that the AirPods will not remain connected to my devices when they are connected to a Mac or Apple USB-C charger. So whenever I am listening to music and plug in the power cord, the music cuts out instantly (first in left ear then in right) and the AirPods disconnect from my device and become undiscoverable until they are disconnected from power. I am using Apple cables only.

This wouldn’t be such an issue, since the battery life is so long and there are few times when I’ll need to charge while using them. But I am also having some strange issue with transparency mode not working well. I would hope a firmware update would fix that. Unfortunately these AirPods are on 4E71. And from what I’ve read, the things will not update unless paired to an Apple device AND connected to the charger, which it would seem it not currently possible with my AirPods. I have already tried a hard reset by holding down Digital Crown and noise cancelling buttons for 15 seconds. It flashes the corresponding lights and generates some tones in the earphones when doing this and then must be manually forgotten and re-paired to my devices so I’m assuming it is successfully factory resetting.

Can anybody please share solutions if they have encountered this issue before. The AppleCare on these has expired and I imagine it’s really spendy to deal with Apple on these out of warranty.

TL;DR: Why are AirPods Max disabled when connected to power? How can I update the firmware in this state?