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.