I haven't done PID for a looong time but the best method for tuning PID loops is to look at the frequency response, somewhat along these lines: https://eng.libretexts.org/Bookshelves/Industrial_and_System...

This is much much better than the rules of thumb of increasing the proportional gain until the system becomes unstable etc. etc. You can tell what your gain and phase margins actually are which is difficult otherwise so you can push the correct parameters to the limit while maintaining margin.

There are also other approaches that rely on modelling the system and calculating the parameters based on the model... That can work but tends to be iffy for real world systems in my experience...