You might be interested in checking out some of the following answers I wrote to related questions:

• This one about how life was like as the USSR collapsed.

• This one comparing Russia's transition to capitalism in the 1990's to Poland's.

• This one about the demographic consequences of the collapse of the USSR in Russia.

One reason I'm linking to those different answers is that there isn't a single definition or benchmark of "living standards". We can talk about economic growth/decline, especially at a per capita level, or talk about a number of public health metrics or even some different "quality of life" metrics, but they don't all line up in the same way.

I'll also note is that there isn't a single answer that will encompass all of the USSR neatly, as different regions went on very different trajectories. Estonia, for example, was a relatively well-developed republic, had a relatively short, sharp economic downturn in the early 1990s, and today is arguably significantly more developed than it was in the Soviet period. Tajikistan, on the other hand, was relatively poor, suffered a devastating civil war at the collapse of the USSR, and by many standards is worse off than in the Soviet era. Even within single republics, there are extremely different trajectories that different groups took. If you look at urban populations in the former USSR in the quarter century since 1991, you'll see that "rust belt" industrial areas, and cities in the Arctic and Siberia that the Soviet government subsidized its citizens to live in, saw big declines, while urban centers like Moscow saw massive growth. And even within regions, the change impacted different groups and generations differently (older pensioners had much more difficulty adjusting than younger people).