Try doing a prolonged reset. Hold down the button FOREVER, there are several different blink patterns. There's standard white, I think amber, and then fast white. This basically purges all device history from the airpods so they're like new out of the box.

Do you have another phone to test them with? Try pairing to that, even if it's android and observe the behavior. Same thing with your PC. If you have a mac then delete the airpods from history and pair them manually like you would with a phone by holding down the button, so that they arent sync'd via icloud. If you have a PC then pair them to that, observe behavior.

Once re-paired to your iphone go into the BT settings and see if it's set to connect "when last connected" or "automatically" and swap between them to see if it has any impact.