https://www.cdc.gov/quarantine/order-safe-travel/technical-instructions.html#anchor_1635183089047
Scroll down to Table 4 "List of Foreign Countries with Limited COVID-19 Vaccine Availability"
As you can see, the list is very limited and Russia is not on it. But you were right, if immigrant visa applicants (i.e wives/husbands) do the medical exam in Moscow, they will get the COVID waiver for limited availability of the vaccine. Their visas would have a note saying they are allowed to board the plane to the US without vaccination. However, non-immigrant applicants (fiancés/fiancées) would still need to get vaccinated somewhere else, as this waiver does not apply to them.
Let me clarify the process for medical examination in Moscow for immigrant and non-immigrant applicants:
For immigrant - You must have all vaccinations prior to immigrating to the US, if you don't have the WHO approved COVID vaccine, you'll get an "incomplete" status on your medical examination and COVID waiver to board the plane, due to limited availability, as mentioned earlier. This "incomplete" status does not affect the visa but when your wife arrives in the U.S. she'll need to complete her medical examination and get vaccinated in the U.S.
For non-immigrants - They get "complete" status even without WHO approved vaccine, Sputnik is enough. My fiancé had his medical exam in Moscow and it was marked complete with the Sputnik. However, he's getting a Pfizer vaccine in Turkey so that he can board the plane to the U.S.
Note that this applies to the medical exam done in Moscow, if you will be completing it somewhere else, the rules will be different. For example, Israel will require you to get WHO approved vaccine prior to completing medical examination there for immigrant visas, because they cannot grant you the waiver for limited availability (Israel does have Pfizer). On the other hand, for non-immigrant visas Sputnik is enough. They will mark you "complete". But you'll still need to get it yourself to board the plane😁
This is ridiculously complicated.