I worked in credit card acquiring business (implemented credit card application for the terminal).

Cards with Mastercard or Visa logo can still work without Mastercard or Visa processing the payments.

Obviously, they do work in ATMs.

For normal payments it is possible for another company to step in and process the payments. That would be massive effort but not impossible to get done in say couple of weeks.

But that would still mean that the system would be cut off from the rest of the world -- cards issued by Russian banks would not be valid outside of the new system. Cards outside of Russia would not work because it cannot communicate with Russian system. And cards issued outside of Russia would not work inside Russia for the same reason -- the transaction would not be possible to authorise across the border.