I fixed my oscilloscope.
The burnt capacitor in the power supply was replaced with a more robust MLCC 0.22uF 500V from Vishay. The problem with the power button was solved by simply cleaning the contacts. BTW, I replaced the built-in ADDA fan with a slightly less noisy one from Noctua (only with the “low noise adapter” that comes in the kit, otherwise it is at least equally noisy). But the main thing with this replacement was that I managed to get rid of the annoying high-frequency trill of the old fan, somewhat reminiscent of the sound of a cricket. I think (even sure) this sound did not come from mechanical parts, but from the operation of the brushless motor driver.
The hardest thing in this whole story was to peel off and then to put this sticker back on so as not to damage it, but I think I managed to do it pretty well.
My scope has been working flawlessly for two weeks now.