As you state, the buzz indicates that there is AC mains leaking into the audio, and your test of touching the case, which stopped the hum, confirms that. Note that your touching the case did not ground it, but rather put your body and the headphones at the same potential as the case... which could be problematic, in reason 2. below.
There are two likely ways that 50- or 60-Hz could get into circuits from the charger:
- There can be capacitive coupling in a nongrounded power supply, either from the mains hot lead, or from high-speed pulses in the switching power supply. That is trivial, and can easily be remedied by adding a 0.1 µF, 300 V capacitor from the third (ground) pin of the mains socket to the PC shell, with a 270 kΩ resistor in parallel to dissipate any charge built up on the capacitor. That is what I did for a Toshiba laptop, which has been working well for years since that wire was added.
- There could be actual mains current flowing from the power supply due to an internal short -- effectively putting your body at 120 or 240 VAC! If you were to touch both the case and a grounded object (e.g., refrigerator, washing machine or water pipe), the result could be fatal.
To check if there is dangerous leakage, connect a multimeter on its AC voltaage range from the USB-C outer shell to ground, with a 0.1 µF cap mentioned above across the meter to lessen any minor leakage current (modern high-impedance multimeter are too sensitive, otherwise). If the meter indicates more than 10 volts, with the capacitor bypassing it, the power supply is, indeed, defective and could cause electrocution. Replace it. N.B.: Use care connecting the meter. First connect the leads, then plug in the supply! Do not touch the wires while the supply is in the wall socket.
