He’s turning quite slow in the video. A scout or cavalry saddle can turn incredibly quickly.
What you do is you do need a little speed, but then you release running forward and turn while the horse is coming to a stop, you can turn nearly instantly with a scout saddle. If timed correctly, you can release forward, turn, and then press forward again with sprint to almost lose no speed at all.
It does take a bit of practice to do it, but it does feel immersive and intuitive so its not a bug. And this can be done with any vanilla/dlc saddle or horse does not need a mod.
As for NPCs being on your tale the entire time, this is a bit of a problem. But no so much on open terrain and using a Cavalry saddle.