Often the manuals leave out the specifics. OTOH, they won't provide all permutations of connectivity either- that's just not practical, given the subtle but sometimes significant differences in how these various wireless devices behave in the real world, regardless of what specs they share.
OK. You can always try a garden variety BT adapter/transmitter & BT headset from Amazon with your 'tuner'. Typically though, you won't be connecting a BT adapter with a mobile device (as in smartphone). It's usually the built in BT of the smartphone sending a wireless signal to either a standalone BT speaker, or larger AV system (e.g. AV receiver with surround speakers, etc.). FM gets lost in that process often since we now have the ability to stream FM broadcasts over the internet with our various tablets and phones.