I would like to play/pause without using the keyboard.
Foot pedal ? … https://forum.audacityteam.org/t/foot-pedals/52288/2
Can I use an IR remote to control playback sessions?
Any device that can simulate a keyboard could work, including your phone. You would probably need an IR receiver unless you went bluetooth instead, which is likely already built in to your machine (and your phone).
Google for a IR or bluetooth powerpoint or presentation device or app.
How do I tell Audacity to listen to Bluetooth?
I do not have all that much experience with Bluetooth.
You don’t. But you can direct Windows to listen for keyboard keystrokes through bluetooth. (Well, actually, Audacity could listen to bluetooth audio - but that is an entirely different subject )
I cannot recommend any specific products, but you could start your search with bluetooth keyboard/powerpoint/presentation app.
The idea is the app will send keyboard commands to your PC. As most phones and computers support bluetooth today, you simply have to “pair” the two devices. You will likely find a youtube video showing how to set up your chosen app.