@Omega Mac When you signed out of/in to iCloud did you get the notification that "Facetime/Messages are enabled to use with your_loginname@whateverdomain on MacBook Pro"? I don't know whether it's a random combination of unknowns but doing that only on one of your devices (i.e., iPhone) may suffice. If you tried logging out of your Apple ID (or iCloud which essentially is the same) account on all devices and it didn't help then I'd suggest taking notice of what the actual names of your devices are that are registered as
Trusted Devices. Do they match the names under
Phone, Messages, Facetime in the phone's
Settings?
As far-fetched and extremely unfriendly as it may sound I was having
Hands-off non-operational just yesterday after a period of inactivity, frequent reboots to other macOS etc. Turned out the culprit was the name of my iPhone that I had changed. I had to unpair both devices in
Bluetooth settings and then pair back because no matter what, the phone was showing as the old name on my Mac which stubbornly refused to see the phone. All attempts to enable
Calls on Other Devices fell flat with an alert to the effect of
Calling on other devices couldn't be enabled. Make sure you're using the correct iCloud account and AppleID on all of your devices even though I used the correct AppleID: after I re-paired devices I regained control over
Hands-off and the constituent services. Before this had illuminated my mind, I had wasted fruitless efforts by re-signing in my iCloud account. I understand it's a different issue and may not work for you but you can try just in case. Regardless of whether it's the culprit, the fact you have to re-pair
Bluetooth devices to make
Hands-off work is beyond silly: you'd think the macOS system would handle that automatically by having some kind of the UID key assigned to a device or your AppleID that ignores changing the device name or display an informative message if it fails to refresh it, but no - you have to guess on your own. Slapdash programming. "Just works?" - Hell, no.
One last thing: are you running Catalina? That could be both the answer and a possible fix which is either to downgrade to the last macOS where everything works (e.g., Mojave), or upgrade to the latest stable revision (e.g. Big Sur) to see if they fixed this issue. However, there could one more factor in play: I suspect that all these issues crop up if you're not using companion versions, e.g. something like iOS 14 and Big Sur. I'm still on iOS 12 and Mojave which were companion releases. This is speculation at best but it could be pretty much real.
If you aren't running companion releases and think it's worth the risk then try upgrading both devices to iOS 14 and Big Sur and see if the issue goes.
