What would a Red Navy carrier actually do?

Would an aircraft carrier be useful to the Red Navy in the Baltic, Black Sea, or Pacific?

Yes, for reconnaissance, fleet air defense, and long-range anti-submarine work, even where it is less suited to a classic strike-carrier battle.

A carrier could provide reconnaissance and fighter cover close to a Soviet fleet. Its aircraft would avoid spending so much fuel flying out from a distant shore base. They could also extend anti-submarine coverage beyond the immediate vicinity of the ships. Those tasks mattered before later satellite, missile, and helicopter systems were available for the same fleet roles. A Soviet carrier's usefulness would therefore depend on its station and employment, even if it seldom fought another carrier.