Heaphone amplifier PSU noise
It sounds ground-loop-ish to me.  I think you need to isolate your audio ground from your input power ground (which is what your power bank does).

Instead of grounding the audio in hard to the chassis of your headphone amp, I would run it to ground with something like a 1k\$\Omega\$ resistor.  Then I would replace your unity-gain buffer with a unity-gain difference amp, so that \$V_b = V_+ - V_-\$, where \$V_b\$ is the buffered voltage, and \$V_+\$ and \$V_-\$ are the audio signal and "ground" respectively.

If you feel paranoid about such a light coupling of the audio ground reference to your headphone ground, you could run a pair of diodes it to +12V and -12V so that if it's anywhere in between those rails the diodes are both reverse-biased, but if it strays outside those limits they'll clamp it.  That would provide some protection (ESD and wiring oopsies both) to your op-amp.

As an alternative, your +5V to \$\pm\$12V supply could be transformer-isolated, but that's a lot more work.