Yes, there was Sunday in USSR, and there was Sunday in other Warsaw Pact countries (which were separate countries with their own peculiarities and differences in living standards, languages and traditions). In fact, there was an entire weekend to relax and rest, and that's a fact for the simple reason that the 1917 October Revolution (not to be confused with the February one) was a worker's revolution, enacted by the Communist Bolshevik party. Almost the entire political platform of communists and socialists, especially if you dumb it down and shout it in the streets (as is the way to gather supporters), was unions, workers' rights, a stop to exploitation, and strict and humane standards for labor. And this was relevant because the working class in Russia balooned enormously in the preceding years: after a delay the Empire was undergoing rapid industrialization on the double, and millions of former villager peasants moved to the growing cities to become factory workforce or man the service sector.

This of course doesn't nearly cover the entirety of how and why the revolution came about or how the Soviet Union formed and then lived. But you can bet your hat that instituting an 8-hour workday and regulated work week was the first item on the agenda, simply because a lot of the propaganda that convinced the people to side with the Reds was about this.

In Russian Empire during the industrialization, work load steadily increased like in the worst examples of British exploitation - very long workdays, no job security or benefits, the worker is at the mercy of the employer etc. It started to get better before 1917 (after all the revolution didn't come out of nowhere, and the push for workers' rights was present decades before), but still was rather wild. I should note that some large and prosperous factories with decent owners actually treated their workers well, and even had choirs and schools and pensions and good accomodations and such (like the great Putilov Factory). Others did not.

In any case, later in Soviet Union labor codex was a very serious affair — just like labor itself was the most sacred and respected concept in the national narrative. As the state gradually pledged to fully supply its citizens with housing, employment, pensions, and healthcare, it also was very particular about workload, vacations, salaries, bonuses and such. (And the work itself — you had the right to be employed, and had the obligation to exercise that right.)

So anyway: in 1917 the new government instituted a 48-hour workweek and a 8-hour working day. This meant Mon to Sat as weekdays, and Sunday as a holiday. That said, at some point USSR indeed did NOT have a "sunday". This is because in early 1930s and until 1940, there was an experiment to institute a 6-day week (5 weekdays and one holiday). This worked in parallel with normal week, like shifts. In 1940, a 7-day work week (6+1) was re-instituted.

After the War, the working day gradually shrank: it started with short Saturdays and pre-holiday days (6 hours), then all working days were made 6 to 7 hours (usually interleaved with a long lunch leave, so effectively an 8-hour day). Finally, in 1967, the 5-day, 40-hour workweek was established, and survives to this day in the successor state Russian Federation and in many former Soviet states, as well as former Warsaw Pact states.

The prevalence of the firm right of a Soviet citizen to a free weekend is exemplified in the notion of subbotnik — a pseudo-voluntary community, school or workplace activity taking place on some of the Saturday mornings. It usually consisted of cleaning up the landscaping, planting trees, tidying up or helping renovate your place of work or study, or simply doing your usual work. Started off as genuine voluntary contribution by motivated workers, in the post-war period it was organized and formal — but still maintained the pretense of voluntary help, since it took place during legal holidays.