Don't necessarily need a solution, just. Documenting weird tech things/curious why it might be happening if anyone has an idea.

Bluetooth headset for computer. PS4 controller plugged in via USB port, using a generic cable.

If I am playing a game, headset stays on and stays with game.
If I have secondary audio running, like a podcast, if I don't put anything else on once the podcast finishes, my headset will go into sleep mode after a few minutes
(So not reading the game as an audio source to stay on for even though the headset is still playing the game audio until it goes to sleep.)

If I turn the headset back on, it does not automatically start playing the game audio again. It will still play other audio if I start it .
Making the game background, then unplugging and replugging in the controller, will make the game audio come into the headset again.
Messing with the controller while the game is the active window will not link the headset to the game.

Is very bizarre