The buzzer is there for both to mark the frequency and signal that it's alive. Its old sequence had a hourly faster buzz which returned to normal at the beginning of the hour. It looked like this

  X:59:00 - Buzzing gets faster.
  (X+1):00:00 - Normal buzzing resumes.

I think it served as a crude hourly sync signal for some systems until GLONASS came and provided atomic level sync. This also implies that there may be other non-human systems listening for this station.

It can be speculated that Russian Perimeter (Dead Hand) system [0] may be one of the listeners.

[0]: https://en.wikipedia.org/wiki/Dead_Hand

The Wikipedia article makes the operation of that station appear to be at a level that is far more relaxed than what I would expect from a really important continuous liveness signal. So I consider the use for something as lethal as the Dead Hand system unlikely, if it even still exists.

If I understood correctly, Dead Hand has many inputs and generally stays off so, maintenance won't create unintended consequences.

If whole system (and world's fate) relies on a single buzzer, we have much bigger problems :)

Would that mean that if the buzzing stops for an extended period, Dead Hand assumes World War 3 is underway and launches the missiles?

According to available information (and speculation), perimeter listens to various inputs (which is a good thing).

It's said that it has connections to seismic and pressure sensors and can check whether communication to critical infrastructure is intact. So it keeps tabs on many heart-beat signals it seems. UVB-76 might be one of them.

Moving a low traffic radio station with an interesting sound just because a bunch of HAM radio guys doesn't make sense. It has to have some higher function to warrant the move.

With the new over the horizon radar systems Russia is deploying, I guess that signals from these would be evaluated too.

Going in to wild speculation territory, Russia's in-house CPUs would fit the bill for these kind of systems nicely.