Alright. I found a spot to get 12V inside the QYT KT-8900, which is pin 5 of the audio amplifier IC. It is located near the entrance of the DC cord. I bought it to pin 1 of the MIC socket, which is unused in this radio: that's where you can push the audio output for Packet/APRS (the documented mods mentioned in the previous post).
The result is that now the buzz is present both on transmit AND receive.
The oscilloscope explained everything. The wireless dongle generates digital spikes on its power supply line. Since it is designed to operate from the internal battery, nobody cares if there are 100mV 500Hz spikes.
Solution: add 47-100uF electrolytic capacitor on the power supply line of the dongle.
Thirty seconds after finding the solution I burnt the receiving dongle. (Hint: capacitors retain the charge.) Actually the LDO inside went short circuit. I removed and bypassed it, but while 3.3V to the dongle do power it up, it does not pair with the headset and shuts down after 10 seconds.
Considering that I am not operating /M on a daily basis as in pre-pandemic times I am now thinking of possible evolutions or restoring the same setup.