When I try to connect my MacBook Air M2 to my iPhone 11 over Bluetooth I get: device not supported

What I am saying is while Apple devices do use bluetooth for many things, there is no need to directly connect or pair them for this. Bluetooth is used as necessary when the devices are nearby to each other. Direct connection is not required nor possible except for Personal Hostpot.

Again, what are you trying to accomplish by connecting them?

AirPlay uses Wi-Fi not bluetooth.

As long as the Apple TV box and your Apple devices are on the same Wi-Fi network, they can talk to each other.

Link-> Use AirPlay to stream video or mirror the screen of your iPhone, iPad, or iPod touch - Apple Support

Link-> Use AirPlay to stream what’s on your Mac to an HDTV - Apple Support

Correct. You cannot directly connect a Mac to an iPhone over bluetooth. What are you trying to accomplish?

The only feature that requires a direct connection over bluetooth and will allow it, is Personal Hotspot.

All other features that require bluetooth between a Mac and an iPhone do not require a direct connection, just that bluetooth be turned on, on both devices.