BT latency is annoying enough when listening to media. I'm used to pressing the pause button and having the audio stop promptly, with no perceptible delay. The video desync (if applicable) can also be very annoying.
That's odd, I have literally never experienced that before. What kind of setup are you using? I just tried it now, thinking maybe I just never really paid attention to any play/pause delay when listening to music or watching videos. Nope, it's pretty much instant as far as I can tell. I'm using the AirPods Pro and had Gen 1 AirPods before that -- can't recall ever having that problem in the past 3 years.
Not GP. It really depends on the device in my experience. My Denon system has seconds of lag over Bluetooth, enough to even make the volume slider on the phone annoying to use. On the other hand, my wireless headphones from Sony have as far as I can tell zero discernable lag. Both used from the same Android phone.
Could be the codec they are using. AptX LL is the best for latency as far as I know, but not all headphones support it, and you have to go into developer options to change it.
The Denon system might be using LDAC which is higher quality, but sacrificing latency.