After a new test, it seems the root of the issue lies in the look vector smoothing, and more specifically in the accumulation values. In the Update void from PlayerInput the horizontal and vertical input values are added to accumulation values, but if the input values are used as they are then the framerate issue may disappear. When using a manual vector like this :
C#:
manualLookVector.x = GetAxis(m_HorizontalLookInputName);
manualLookVector.y = GetAxis(m_VerticalLookInputName);
The camera rotates simply with no smoothing but consistently regardless of the framerate, and AdjustForFramerate is not necessary.
When using raw vector or Unity smoothed and removing the plus symbols in update, the AdjustForFramerate bool does exactly what it is supposed to do.
C#:
m_RawLookVectorAccumulation.x = GetAxisRaw(m_HorizontalLookInputName);
m_RawLookVectorAccumulation.y = GetAxisRaw(m_VerticalLookInputName);
m_UnitySmoothLookVectorAccumulation.x = GetAxis(m_HorizontalLookInputName);
m_UnitySmoothLookVectorAccumulation.y = GetAxis(m_VerticalLookInputName);
I haven't managed to use FastSkillTeam's code yet, but I'd first like to focus on trying to solve this issue. I'll resume the test tomorrow and try to get some results. And please, once again, it would really help if somebody could just take five minutes and try with a controller on their end, whether this issue happens on somebody else's side would be a huge piece of info !
Edit : Forgot to add, I'm still testing on UCC 2.4.8 and bought UCC 3 as soon as I could, but the framerate issue with the controller is still present in it as well.