How to set Bluetooth headset priority order

A comment on a problem that has come up repeatedly in this and other forums. I have a new set of Phonak hearing aids that are not "made for iPhone" but have the ability to connect as a Bluetooth headset so that they can be used to receive and answer phone calls; the idea is that a call rings in the hearing aids and the button on the back can be tapped to accept the call. I also have a Garmin D2 Air X10 watch. I found that the hearing aid would not receive incoming calls no matter what device type I called them under Bluetooth settings, no matter what settings I used for call audio routing under hearing devices, or by routing to Bluetooth Headset under Accessibility/Touch. Once a call was accepted on the phone, I could then switch it to the Phonak hearing aids by opening the Control Center and selecting them from the list of audio devices available for the phone call, but the calls were actually going to the Garmin watch. If the watch was turned off the Phonaks worked correctly. Evidently, the Garmin watch was identifying itself to the Bluetooth protocol as a headset; this is not a user-modifiable setting. Thus there were two items connected to the phone by Bluetooth both identifying themselves as headsets, and the watch uniformly took priority. There is no direct way the user can assign priority among devices of the same category. You will find some answers to this issue on line that claim that if you unpair and re-pair a device it will go to the top of the priority list. HOWEVER, at least on my iPhone 13 Pro Max, iOS 15.6.1, this does not work. Bluetooth lists, both the main one under Bluetooth and in submenus like available devices for streaming or phone calls, are in alphabetical order. If you select the devices you want to prioritize from the main Bluetooth list, select the Information menu, and re-name the devices appropriately, then shut off and restart Bluetooth and reconnect the device, they will now function in the priority order you want. So my hearing aid remains the default "R Phonak Hearing Aid" but I renamed "D2 X10" to "X10" and now the hearing aid catches the incoming calls....