P should not affect that or at lest not be used for tuning how fast the gimbal reacts to stick commands.

If you use Angle mode, then the gimbal is supposed to turn to the target angle as fast as possible. You could use limit acceleration under basic tab and maybe speed on RC settings. (if it overshoot, the speed/acceleration is too high and probably in your case P too low.) I have not experimented with angle mode, I am using speed mode.

On some radios you can also adjust how fast the the stick movement is sent, but I would in any case suggest having more gentle touch on the stick ;-).

As I understood and understand what you describe is that when you give fast full stick command it overshoots and my answer is to that. If this is not the case please specify.

Is the gimbal working otherwise ok? I guess not if you have P 0 or 1. You should have it working perfectly before starting to use the RC commands.

Have you tried limiting the acceleration and speed? Also make sure that RC angle limits are not causing problems. I have maxed out the RC min and Max values, so they they are not limiting the functionality.

What kind of 'I' values are you using?

Does it work better in speed mode or if you move the stick slowly?

But really, first thing is to get the Yaw axis working good before even trying RC command. When starting to use RC command you should not need to touch PID or Power values. (maybe some fine tuning to get everything move smoothly, but no big changes)

Anyway sounds like you need more power to the yaw. Might be also that you have a broken motor (one phase missing). You could verify this with multimeter.

The Yaw axis is the heaviest to move, it has most mass and inertia. It needs most power of all the axis. It is a super important that Yaw axis is well balanced. i.e. stays in any position if the gimbal (airframe) is tilted 90 degrees.

Especially 'I' value tuning is much different in FW 2.4 than 2.3.

I did what the video has shown.
Set P=0; I=0; D=0 and start increasing the power value. 80 seems to be a good value with enough torque to hold the camera no matter how fast I move. So 80 it is (tried with 120 as well).
Now I increase D until there are micro-vibrations. I can increase it up to 40. (tried the full procedure with values between 12 and 40).
Now I set the P value to 1. The YAW moves correctly and slowly to the zero position.
I gets set to 0.01, everything fine.
If I move the gimbal slowly or move the RC stick slowly, everything is fine.
As soon as the movements are faster it starts to oscillate.

The higher the P value is set the worse it gets. And this makes sense, high P value mean going to the target pos faster with the tendency to overshoot. But the P value is set to 1, it cannot be a smaller value. And that is the root cause in my opinion.

Accel is limited anyhow but first you cannot change it for individual axis. And speed mode might be a workaround since slow movements are working but I would love to have a solution, not a workaround.
I will check if I can set the speed to something that low so that these oscillations do not happen, at the moment it is set to 10 and that is too fast.

Copters work a bit differently I have those too ;-).

But the speed and acceleration are the right way to tune the RC response. PID is more for tuning the gimbal response to external disturbances. (on 2.3 'I' had role on RC response too and maybe still on 2.4, the user manual is not clear on this.)

I see it like this:

1. The primary function of the gimbal is to eliminate the external pitch, roll and yaw disturbances. that need to work well first.

2. Follow mode or RC control are secondary functions though very useful. The gimbals primary function, stabilisation needs to work well first before starting to use them.

Now, if in follow mode or RC mode the speed is too high the gimbal motors can not handle it. That is why the speed and acceleration need to be adjusted to reasonable limits and those limits depend of the motors, frame and camera in question.