As a reminder, the PlayStation Portal, or Project Q, is (according to leaks) based on Android. It doesn't run the games itself, it merely streams them from your PS5 and your handheld then serves as a controller with its own display.
I'm wondering why anyone would prefer that over simply using a regular Android phone with a good controller and the PS Remote Play app?
Standard Bluetooth latency sucks, and would doubly suck having to stream the audio-video to the handheld and then Bluetooth it to the headphones. That's why high end wireless gaming headsets game with a 2.4ghz dongle instead of using bt.
The thing has an audio jack. You could literally buy wired headphones/earbuds from the damned dollar store if you don't already have a pair lying around and then have 0 latency. It would be dumb to use anything for a handheld like this besides wired headphones.