Bode plots and load step response of MPM3690-20B

I measured the Bode plots and load step response.
The phase margin was about 20deg and the ringing frequency of the load step response waveform was more than 7 times, although it might be due to the load capacitors connected about 2000uF in total.
Normally, when measuring Bode plots, the injection amplitude is set at 10 mVpp. When the injection amplitude was set to 100 mVpp as a trial, the phase margin satisfied 45 deg. The amplitude of the load step response waveform was also about 10 mV. Due to the limit of the current that can be injected, it was not possible to input a larger amplitude than this.
Please let me know how much is the correct injection amplitude for Bode plots measurement and load step response waveform measurement of MPM3690-20B with COT control.

I have a further question.
There is an argument that COT control is, in principle, guaranteed to be stable. If this is the case, does it make sense to use bode plots to determine the phase margin?