Cash ( Dollars) might have been king in the Yeltsin years, but that was 18-20 years ago? Times change
Contactless
Apple Pay
Is what most modern establishments in the capital use. Including my favorite bar / hangout.
The problem you will have is with CHIP and PIN if you have a US credit card. Be prepared to sign the a long scroll of paper, and some awkward stares. People are not used to it.
The one thing I like about Russia, is they are really proud of the Ruble and local legislation does not permit dynamic currency conversion, which is forced upon you if you have a Euro/Dollar card in places like Dubai etc. All payments must be made in Rubles.