Amplitude influence in the output signal in inverting op-amp
You've discovered the phenomenon called "slew rate".  The small signal bandwidth is exactly that, for small signals.

When the amplitude gets larger, there's a large signal phenomenon called slew rate that limits the dv/dt of the output voltage.

The reason for this is the compensation cap that forms the dominant pole in the amplifier.  There's a limited amount of current to charge and discharge the compensation capacitor, so when the input voltage dv/dt exceeds what the current source can supply to the compensation cap, the output slews at a rate governed by I=C*dv/dt.  This makes a sine into a triangle at some value of frequency and amplitude.

The derivative of Asin(wt) is Awcos(wt) and the maximum of the derivative (max rate of change) is Aw so A*w must be less than the rated slew rate of the amplifier to avoid any slew rate distortion.
[Edited to correct initial brain fade.]

Here's a link