The Russian fermented bread drink is called kvass.
Kvass is a mildly alcoholic, sweet-and-sour beverage traditionally made from rye bread, rye flour or malt. The grain mixture is soaked in hot water, then fermented with yeast, often with added sugar. Traditional batches may ferment for roughly 12 hours or longer, depending on the recipe and desired flavor.
The drink has deep roots in Eastern Europe. A written mention appears in the Primary Chronicle in connection with the baptism of Vladimir the Great in 988. Kvass became an everyday drink in Russia and neighboring countries because grain was widely available, while beer was not always practical as a daily beverage.
Modern commercial kvass is often treated as a soft drink and typically contains very little alcohol, around 0.5% in many products. Flavors may include berries, herbs, honey or mint. Sourdough is not the answer: it is a fermented bread mixture used for baking, whereas kvass is the beverage made by extracting and fermenting grain-based ingredients.