There is no reason to "pair" you iPhone to you Mac.
The functions that require bluetooth (namely AirDrop, Handoff, and AutoUnlock) do happen over bluetooth connection, but they are not "paired". So, even though it does not list your devices as connected in Settings or System Preferences as a devices being "paired" they are communicating. This communication is done via iCloud servers, local wifi networks, and bluetooth.
iPhone and Mac Bluetooth pairing.
If you notice, in Apple's article Use Continuity to connect your Mac, iPhone, iPad, iPod touch, and Apple Watch - Apple Support it does not list "pairing" as a requirement for setting up Handoff. The word "pair" does not appear anywhere on the article. This is because "pairing" is not needed for this function. It does, however, require that bluetooth is simply turned on as well as wifi, handoff, and iCloud being signed in.
So, if you are having trouble with any of these features, and your bluetooth is turned on, ensure that the other settings are set up as needed.
System requirements for Continuity on Mac, iPhone, iPad, iPod touch, and Apple Watch - Apple Support
Automatically unlock your Mac with your Apple Watch - Apple Support
Use Messages with your Mac - Apple Support