AirPods Pro 2 version 6B34 won’t update firmware

These are the earlier version of the AirPods Pro 2 with the lightning connector (not C). I want to use the hearing aid function on these AirPods as a back up for my current gen2, and I know I need a firmware update (the Bluetooth details told me so), but I cannot get the update to take. I have followed Apple’s directions to update, including

• Connect closed case to charger
• Make sure iPhone (16 Pro) is up to date
• Keep the phone close to the AirPods and on wifi
• Wait at least 30 minutes. (Last time I waited over an hour.)

And if that doesn’t work

• Forget the AirPods in Bluetooth settings
• Repeat the above

These AirPods are new to me but I have verified by serial number that they are authentic. However, when I first connected them to my phone, they did not show up in a separate window, nor do they show their charges when I reconnect like my newer (older to me) gen 2, C connector pair do. These new ones were recognized as AirPods and stored that way in the cloud, but they are not acting like other AirPods I own and more like cheaper brands - which I also own.

Any help is appreciated.