Q: Is it true that Ivan Ivanovich Ivanov from Moscow won a car in a lottery?
A: In principle yes, but:
it wasn't Ivan Ivanovich Ivanov but Aleksander Aleksandrovich Aleksandrov;
he is not from Moscow but from Odessa;
it was not a car but a bicycle;
he didn't win it, but it was stolen from him.
There was no problem whatsoever with buying such things like bread or local fruit. Why? Because a great share of those was produced by private entrepreneurs and had the price set by an almost free market.
Actually you can have a look at the statistical data and you will see that there were more pigs, cows, milk etc. then than now.
The problem was with many products manufactured by the collectively/state owned enterprises, because the prices were set artificially low centrally. That caused lack of balance in the market. Of course you could buy those products paying market prices to the private entrepreneurs (called speculators by the government) in the free market (called gray or black market by the government).
And I can assure you that Pepsi was sold in regular (not Pewex or Baltona) stores and those stores were state owned or controlled by the state (cooperatives) because private stores were almost nonexistent.
I was born in "the Eastern bloc" and Pepsi (Pepsi-Cola, Mirinda) was present in stores in my region. One could buy Coke too but its availability was limited.