iPhone 11 Pro with not Pair with iMac or MacBook Pro (Monterey)

My iPhone 11 Pro (15.3.1) will not pair over Bluetooth with either our new iMac 24-inch, M1, 2021 (Monterey 12.1) or my MacBook Pro 16-inch, 2019 (Monterey 12.3)

I'm trying to use the Continuity Camera feature to scan documents but I cannot get the iPhone to pair with either computer.

Both computers exhibit the same behavior when trying to pair. It is the same behavior reported in this post: Bluetooth connectivity to iPhone 11 Pro M… - Apple Community

In Bluetooth, each device can see the other. If I try to pair with either Mac using my iPhone I get a "Pairing Unsuccessful, MacBook is not supported" message. If I try and pair to the phone from either Mac I get a pairing number which I also get on the phone and press "Pair" but this then fails.

I have tried disabling and restarting both wi-fi and bluetooth but this causes no change in behavior. Always the Mac (either one) appears to connect for 1-3 seconds and then returns to a "Not Connected" state.

I have tried booting both computers into Safe Mode but the behavior stays the same on both machines. No matter what I do I cannot get the iPhone 11 Pro to pair with either computer.

What should I try next?