Triac dimmer makes audible noise (hum or buzz)
I have used some electret microphone (with amplifier) to localize the source of that buzzing. Thanks to Sunnyskyguy EE75 for the this tip.
Well, I found not one but several parts that were making the buzz :(  


inductor L1
ceramic capacitor C3
trimmer RV1
trimmer RV2 (the main trimmer for brightness)


Possibly some others, but these were the loudest.

Unfortunately this is beyond economical repair.