I don't know specifics about Bluetooth control. Is it a standardized protocol? Or does every manufacturer get to implement their own protocol?

I am thinking the answer is no. If it were like CEC, and manufacturers were forced to comply to an industry standard, in guessing we would have already seen this happen.

Harmony hubs were able to control PS3 and PS4 via Bluetooth, but as far as I recall, that is the only system I have used that had any kind of Bluetooth control option.