The way you stated the question presumes democracies and one-party states are mutually exclusive. Keep in mind that Marx and Engels generally did not view party plurality as an essential element to democracy. Instead, they called for the establishment of a "revolutionary dictatorship of the proletariat" in which the proletariat holds ultimate political power . Whether the dictatorship of the proletariat takes the form of a party, trade union or something else was a point of contention for later Marxists.^(1)

As for the nature of democracy in the Soviet Union I would recommend u/Kochevnik81's answer.