First half of the video is without a PID controller. The second half is with a PID controller. Notice that the ship can quickly and accurately fly in the target direction without overshooting.
I use PID controllers for almost everything I make in some way or another. If you have something physics based and need it controlled in a responsive and predictable way, a PID controller is your friend. It will change inputs to match the target as fast it can, but also be smart enough to dampen and counter inputs so as to not overshoot.
The PID controller I've been using/reusing for years is based off of the code in this Unity post. https://forum.unity.com/threads/pid-c...