Most economic figures are easy to externally verify, including these. Inflation is based on CPI which, in turn, is based on the price of a fixed basket of goods. You can literally go buy this basket of goods and verify its change in cost (inflation) over time. And real wages are similarly easy to ballpark to a high degree of confidence by simply looking at the aggregate wages offered in job postings.

As a side note this is also the point of things like IMF, World Bank, etc also publishing their own numbers. They don't simply ask each government what their numbers are, but independently work to determine the numbers themselves using as reliable of source as they can find.

I'd also add that when the mega sanctions bomb initially hit, the official numbers from Russia were actually more grim than those being published by the IMF/World Bank. That was exactly the time when the motivation to lie would have been, by far, at its greatest for Russia since consumer confidence (and confidence in the currency itself) play an ostensibly significant role in such scenarios. Yet they continued to publish honest, and even pessimistic, numbers.