Conflicting information about COVID-era international travel to Russia

My family (dual-US-Russian citizens) wants to travel from Chicago, US to Moscow, Russia this summer to visit our grandparents, but we have gotten very conflicting information about whether this is possible:

KAYAK/Google Flights show the normal set of tickets for every possible date.
The Russian Embassy claims that these tickets do not actually go through, and that the only way to get to Moscow is through a special, ad-hoc, Gosuslugi-managed Aeroflot flight that departs from New York to Sheremetyevo every so often.
Flightradar24 confirms the existence of this flight, but also shows a small number of other passenger flights to the Moscow airports, such as a series of flights from Instanbul to Vnukovo. Their status is unknown, and the Vnukovo website doesn't show them, but the Turkish Airlines site does (?).
Additionally, some of our Russian friends have confirmed other ways of getting into the country. A friend leaving Sheremetyevo a few days ago said that he saw an arriving flight from Europe. Other friends claim that people are entering the country through Minsk (where the government doesn't acknowledge COVID), and only then flying to Moscow. And yet others claim that no flights exist.
To complicate things further, the Russian Embassy COVID information site claims:

Effective March 16, travelers from the United States to Moscow are subject to a fourteen-day self-quarantine

However, we have not been able to find information about whether this is still in effect across all of Moscow's airports, and how this quarantine is enforced. Moscow has recently lifted nearly all of its COVID safety measures, but whether this applies to the international travelers quarantine is unclear.

Can anyone shed some light on this complicated situation?

Best Answer

Russia is not open yet for international visitors, unless they travel for medical purposes or to support a disabled relative.

It's possible that air companies will sell tickets for future dates hoping that admission rules will be relaxed by then, but nobody can be sure when that would happen.

If you hold Russian citizenship you can enter the country all right. Leaving may be tricky but already possible, to reunite with your family. You may need to self-quarantine for two weeks. You may need to prove residency in proximity of a city where the flight is going.

The special flights you are talking about are repatriation flights.