Marco was [probably] right.
Following advice from the Synology support I did some dust cleaning (and some usual, not published) magic gestures like taking memory out and putting it back), and also did something beyond the advice - I've added the 100Ohm resistor to the MB (some images of this OEM "hack" were posted on one of Siglent user forums). This solution is proposed by Intel whitepapers. Server now runs fine for 24h+ on HDD SMART tests. So, crossing my fingers, I can report that the server is OK now. Thanks to all contributors.