I'm not sure about the rechargeable aspect, but for programmability you could use a small IR receiver placed in the center of the LED array. You really only need a one way data transmission and something like Bluetooth is overkill.
I love simple light-based data transmission stuff. I've seen it included in things like guitar pedals that have just a few config bits that someone might want to change infrequently. An app to change some settings can be as simple as just a little webpage! So simple!
Here's a (tiny) demo of this for my PCB business card project from years ago [1]. If IIRC this proof of concept was as simple as using a phototransitor on a GPIO connected to the UART peripheral with a very low baud rate.
Concerts with audience-worn LED bracelets regularly shoot out LED floodlights to the IR sensors on each wrist. Being able to do something similar on people’s ears could be cool.
If you use visible light, then one can use a phone (screen) to blink the pattern to transmit data.
An LED can also be used as the sensing element, just need access to both anode and cathode. Charge the LED and measure the discharge time - it is dependent on light in.
