First I'd note that sometimes English translations of Svetlana Alexievich's books can be a little wonky.

Second, I'll offer up for consumption an answer I wrote on the differences between American and Soviet food intake from the 1960s or so on - which is helpful given that it's basically the late Soviet period is the time period for most of Second-hand Time.

To pull out from that - while food supplies in the late Soviet period were much better than in the Stalin years, and Soviets on average even consumed more calories than Americans, this was heavily weighted towards things like potatoes and bread, and items like fish were consumed much more widely than meat. In the specific case of meat, a lot of what was consumed was consumed in sausage form. Some of the more popular examples can be found here, and you can still find versions of these in stores in Russia and the former Soviet Union, or Russian supermarkets internationally. Some of these common versions are Doctor's sausage, Odessa Sausage, Hunter's Sausage, and Tea Sausage.

I suspect this is specifically what the translation means when it keeps talking about salami. What I'd note is that these sausages are in many cases technically a kind of salami, I guess, as in they are cured pork product sausages, but they're not Genoa Salami, let alone the version of Genoa Salami that tends to get used as a deli meat in North America. They're closer to Bologna, but even there it's not 100% the same as the North American version.

Doctor's sausage in particular was perhaps the most important type of sausage, and was promoted by the Soviet government by design as a means of giving Soviet citizens a source of fat and protein cheaply (the name being basically a form of Soviet advertising, ie that doctors would recommend you eat it for your health). Interestingly it was based on American bologna, as then-Commissar for Internal and External Trade Anastas Mikoyan had traveled to the United States in the 1930s to learn about the food industry, and had imported recipes for things like bologna and ice cream, while tweaking them for Soviet tastes (doctor's sausage was made from beef, pork, salt, milk, eggs, sugar and cardamom). Interestingly the recipe was literally diluted in the 1970s, and this was a source of endless unofficial griping.

So, part of what you're seeing is that sausages in general are a big deal even today in Russian cuisine. But specifically in the late Soviet period, the average citizen would be consuming only a limited amount of meat, and most of that would be in sausage form, and eating good quality sausages would be an added bonus on top of that. This wasn't necessarily anything guaranteed when you walked into a shop. It wasn't necessarily so much about social class at that point as connections - by the late Soviet period a vast amount of the economy and society in general operated informally via blat (social connections/favors) - you basically had to know someone and/or have something you could offer as a favor or a source of barter in order to guarantee that you'd receive a good or service of reasonable quality.