I would have to hear it be able to offer a valid opinion.
I was unable to quickly find recording with such type of siren. Everywhere in sounds libraries is more modern "western type" dual-tone signals. If you can find some russian films from 1960's-1980's where fire trucks at work is pictured, almost certainly it will be such type of single-tone signal.
If memory serves me correctly, in film "Укрощение огня" ("Taming the fire" or "Wildfire" in English translations, 1972, film about early stages of Soviet space program) there was scene where fire trucks speeding to a rocket start position after accident, with such a signal. If I will be able to find that disk tomorrow, I'll try to cut this fragment. Not sure that I still have it, though.
You live next door to Kremlin? lol ;-)
Not always a joke. I used to live (since I was born to 1981) in a building within 200-300 meters from Kremlin, with windows looking to Borovitskie gates and Big Stone Bridge.
Not a best place to live, of course.