The transformer will saturate when the magnetizing flux reaches a threshold - the magnetizing flux goes up with lower frequencies and higher voltages, since the magnetising current sees the inductance of the core. Larger cored transformers can handle lower frequencies and/or higher powers. The sudden rise of distortion at the low-end is thus magnetic saturation in the transformer core.
The baseline increase of distortion with power is likely to be circuit-related as its independent of frequency. That might indeed indicate class A to AB transition somewhere above 1W, but I think you’d need to plot in more detail at lower powers to get a better feel for this.