Nintendo Switch's audio input to wireless headphone buzzes when Switch HMDI contacts the monitor input

I'm pretty confused. I can hear the Nintendo Switch output via the radio transmitter (Steel Series Arctis 7) clean, but as soon as I insert the HMDI from the switch into the monitor, I hear a rather loud, constant hum. The line for the transmitter is bad, but why on earth does the HMDI connection cause this interference?

Note that there is only one HMDI input to the monitor at a time, and the radio transmitter is always connected to a PC.

Update: I fixed the buzz by just turning up the switch volume, but I'm still curious what would lead to that.