I had hoped to have a demo for you by Christmas, lol, but that did not happen.
Please forgive the long delay, but I've uploaded a demo that you can learn from.
https://tadgames.itch.io/space-shooter-dog-fight-demo
The players rotation will work at full screen and at no scale, but not in between, the code would have to be edited for it to work when scaled in between.
It uses just basic trig to make it seem like the enemy plane is thinking. If the player is really close to it, then it will start to circle the player,
when the player is away from it, it follows a pre-defined path.
You can use the source code to make your own game, free/commercial.
What took so long is that I was trying to finish the documentation as well, but I'm still working on the docs, which will take some more time.
I hope the demo gives you some good ideas.