How to animate gameplay camera?

I wonder how the gameplay camera animation is done. For example, I have a basic character setup where I can move the camera with the mouse in all directions without any problem, but at some point the character gets “fatigue effect” and I want the camera to smoothly look down, and while the character is tired, lock the axis rotation Y. When fatigue is finished, smoothly return the camera to the horizontal position and unlock the Y axis movement.
For better understanding i captured Dead By Dayligh video that shows the exact behaviour (there is even little camera shake while fatigued): https://youtu.be/LV80fasHw0c

You will have to set a fix value for the Pitch (move up and down mouse)

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Use your input event mouse, add some condition and then set a fix value to face a little bit down.
With a function timer for the cooldown effect of the fatigue effect.

There is even better way (imo) doing it thourgh camera manager, but question is more about animation and smoothnes of that. I could somehow manually animate it through code, but that does not seem to be smart. Also those shakes, but i guess they are made with camera shake source and thats good practice.

You can just use function timer with a lerp to animate the camera to look down.