The TV controls for both the Fire TV and Tivo remotes use IR since that's the native technology understood by the TV itself. The only interesting part is getting the buttons on the remotes to trigger the emitting of the correct IR codes. Databases of IR codes seem to be a pretty organized thing these days. Our TV is Sony, so it's pretty mainstream.

Besides the BT and IR things, there is one other interesting protocol in the mix, which I mention only to describe how I don't care much for it. The TV and all of my media sources use HDMI. They also all support a feature called HDMI-CEC ("consumer electronics control"). That's a protocol where one device can send commands to another device over the HDMI path. So, for example, the play/pause, fast forward, and rewind buttons on my DirecTV remote can control those functions on my streaming dongles (after I switch the remote to TV mode). 

Nice. Well, nice-ish. 

Even for my small menagerie of devices, there is a lot of quirkiness in their compatibility with HDMI-CEC. HDMI-CEC also has a limitation on the number of devices that can participate. (It's a limitation of the protocol, not any particular device's implementation.) If you go over that limit, it's hard to predict what will happen. I found that out when one day, after a harmless cable re-arrangement, our TV suddenly refused to connect to our sound bar. After hours of fooling around, I hopped onto my Internet machine and found out about the protocol limit.

The other quirk of HDMI-CEC (or possibly just the devices I happen to have) is that there is sometimes a small but noticeable delay. It's kind of annoying when you do volume up or down and there is a fraction of a second delay before the equipment reacts to it. I guess it's a little bit of Life in the 21st Century, but we have low tolerance for lag, even for things that should seem kind of amazing when they actually happen. But, compare that to 20th century technology, with fewer cooperating things in the path: you'd be stunned if a device didn't react instantly to its volume controls.

I still have HDMI-CEC enabled for all the devices, at least up to what I now know is the numerical limit. But we don't use it for most of the controls. It is nice that, when I press the "Home" button on either of the remotes for the Tivo Stream 4k, the TV and sound bar turn on and the TV switches to the input port for the Tivo. Beyond that, meh. (One surprising and undesired side-effect we discovered was that using the volume controls on the Fire TV remote -- the one being used with the Tivo -- causes the TV to switch to the Tivo input.)