My guess would be that the buzzer is so that the listeners know the station is still "up" and hasn't been destroyed

Or to keep the frequency free from other transmitters, as described in the article

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.