Cannot connect home phone to my iPhone via Bluetooth

I have an AT&T CLP99483 DECT 6.0 Phone/wireless extension/answering machine combo. One feature of it is you can pair your cell phone to it via Bluetooth to use the AT&T phone effectively as a headset.

I have tried to pair 3 iPhones (2 iPhone 11, 1 iPhone SE 2020, all iOS 14.7.1) and only 2 of them work (surprise, the one that doesn’t work is mine! – one of the iPhone 11s) It’s a pretty simple setup: go thru the phone menu to put it into pairing mode; on the iPhone go to Settings -> Bluetooth and the AT&T phone shows up in available devices. I can’t figure out how my iPhone is different. Suggestions as to what is blocking the BT connection on mine? I already have 7 BT devices under “My Devices” but only 1 is currently connected (my Garmin watch).