how does the psvr know if you are standing?

It depends on the placement of the PS Camera relative to your/headset position. You will have to position your camera at a height similar to your height in the chair in order for the camera and game dynamics to think you are standing. This is done while launching the game. You gotta calibrate it by matching up the position, which shouldn't be a problem as long as the camera is aimed at you and your head somewhere towards the upper center of the picture.

It does not actually make difference whether in the game you are standing or not. The position of the camera and yourself can still be same whether you're playing Farpoint, COD Jackal Assault, or Air Force Special Ops. You can stand for a sitting game and sit for a standing game. I occasionally sit on a rotating bar stool if I'm tired of standing. The only standing games that actually require you to stand are the more physically demanding games like the boxing games. You could play Beat Saber while sitting.

It doesn't. At least the Oculus Rift doesn't. After all, it has to work for people of all body sizes.

Only problem you'll encounter will be, as in real life, in room scale VR where the games needs you to move about in the room. With the Rift, though, "room scale" for me usually means I have to be careful if I stretch out my arms.

And just keep in mind that with the PSVR you still need to stay within cable range of the box.

It doesn't really, depending on the height and angle of the camera, you can appear to be higher or lower than in reality. Games that are standing only just assume you're standing, you might have a few problems as some standing games require you to turn around or duck very low which I don't think would be easy in a wheelchair.