After a long and tedious process of tuning parameters, I have observed that the Ackermann car is undoubtedly much more sensitive and unstable compared to the holonomic car. Additionally, the speeds applied to the holonomic car are reflected much more slowly in the Ackermann car.
The change in PD constants for angular speed, depending on whether the car was on a straight or not, has been disabled, just like the I controllers, as they did more harm than good in some circuits. Finally, I have kept the most robust version.
In any case, the final results obtained for the Ackermann car are as follows:
These are not particularly fast lap times, but increasing the speed would result in not completing the more complex circuits and experiencing large oscillations. Therefore, these are the best results I have achieved.