Class D amplifier output signal
No, this is a "filterless" amplifier that relies on the electromechanical filtering of the speaker itself to produce the correct acoustic waveform from the digital output signal you see on the scope.

Unlike most class-D amplifiers that use PWM to drive the output stage, this one uses delta-sigma modulation. This eliminates the strong tone that occurs at the PWM frequency with conventional amplifiers that needs to be filtered out by additional passive components.

Your power supply needs to be able to provide the transient currents required by the audio signal; you basically need more bulk capacitance close to the amplifier chip(s).