Yes, I would say the absence of frozen wake in your approach is the reason for the offset.
FYI: Similar questions have been discussed in past forum topics, e.g., see:
I asked internally how this is handled in ROSCO (GitHub - NREL/ROSCO: A Reference Open Source Controller for Wind Turbines) to automate the calculation of pitch controller gains, and @Daniel.Zalkind confirmed that the pitch sensitivities are computed numerically based on the Cp surface, like you have done. I’m a bit puzzled myself how this would work, especially near rated where the pitch sensitivity will be near zero with equilibrium wake, but where the pitch sensitivity will be nonzero with frozen wake, which is preferred.