I've never seen a mechanical keyboard that wasn't loud; let alone silent. (The thread topic is noise, not comfort or usability.)
That doesn't mean they don't exist. Maybe if I rubbed shoulders more with the high society, I might get access to some invitation-only showroom for exotic keyboards where $14K will get you a whisper-silent unit.
I do have one almost absolutely silent keyboard. It's quite awful to type on. Basically it's one of those flexible rubber keyboards for industrial environments, where there are spill and dust hazards. I use it at night, not to disturb anyone. I optimized for sound at the cost of comfort.