When you bring up the option to turn off your phone, there's a toggle to let you turn off "Find my iPhone", with a decent description:

"iPhone Findable After Power Off >"

> iPhone Remains Findable After Power Off > Find My helps you locate this iPhone when it is lost or stolen, even in power reserve mode or after power off. > > The location is visible in Find My on your other devices, and to people in Family Sharing you share location with. > > You can temporarily turn off Find My network and it will resume when this iPhone is powered on again. > > OK > Temporarily Turn Off Finding

If you click Temporarily Turn Off Finding, you need to enter your passcode. This is to prevent phone thieves from just turning off your phone to make it untraceable.

My expectation is that if you Temporarily Turn Off Finding, the bluetooth radio is fully off.