If the amplifier plays "tadat, tadat, tadat" when its audio is connected, playing or not, then of course its current will be bouncing all over the place. Instead of measuring the USB current, it would be better to measure the USB voltage that is probably also bouncing all over the place when it should be steady and regulated. If the USB voltage is not bouncing then the audio or its ground is bouncing.
The amplifier's input plug has a tip, (left input), ring (right input) and sleeve (ground). It seems that if the left input of the amplifier is connected to the ground or the audio output of the laptop headphones output jack then the problem occurs.
I suspect that the USB +5V is poorly regulated and also powers the headphones output amplifier. When the TDA2822M amplifier draws current to play the headphones signal then the USB +5V collapses a little which also causes the headphones output DC voltage to change. Or the ground voltage to change.