Yes this is a classic "ground loop" example.
The root problem is that the ground voltages at the DAC and at the amp are not the same (the difference is the noise) but are connected together tightly in the PC's power supply. This voltage difference is applied to your unbalanced interconnect cable where it forces a heavy current through the shield and that's where the noise is actually created as an audio signal. With better cables (low shield resistance) the noise is less, but won't go away.
You have to "break the loop" literally, unless all the supply voltages and the ground they are referenced to come from one single point.
This can be done in several ways:
1) Insert audio isolation transformers in the connection from DAC to Amp. Might be not an audiophile solution unless expensive transformers are used (Lundahl, Jensen, CineMag, Sowter, ...) and choice of model is critical.
2) Insert an USB Isolator that has enough power to supply the Khadas.
Intona's USB Isolator might work well and is reasonably priced though not exactly cheap (I use it on a daily basis but haven't tried bus-powering anything from it, specs say it is good for at least 300mA).
3) Somewhat cheating, but still might work good enough at very low cost:
- Use the best and shortest(!) audio cables between DAC and amp, and add an additional thick(!) ground balancing wire that attaches to the (audio) grounds of these two devices. We want to make the resistance of this ground path as low as possible.
- Use the longest and cheapest USB cable in an effort to make this (parasitic) ground path high resistance (relatively speaking) so that it does not dominate. And it is a very good idea to wind up the cable as a coil, preferably on a large ferrite toroid core, or on a laminated core salvaged from an old toroid power transformer.
We want the noise voltage to be dropped along this path, not along the audio signal path.