While some parts of Russia escaped devastation (Smolenschina, Polotsk, Novgorod), most of it did not. Kiev was in steep decline, yes, and the Severian lands were often raided by the Vladimir princes, but the two heavyweight centres of power (Galicia and all of Vladimir-in-Zalesye's regional centres) were very very thoroughly ruined.
Ryazan was never rebuilt in its old spot. Vladimir never recovered its importance. Kiev, Kursk, Novgorod-in-Severia, Chernigov etc. remained unimportant until the 18th c., 17th if we're being generous. Tver and Moscow were small and took the opportunity to overtake their rivals, but at the expense of other cities that were on the up before the Mongols.
Russian colonization beyond the Dniepr and on the Don and Donets was completely halted. Archeology confirms dozens and dozens of small towns (a couple of thousand settlers each) that were ruined and never rebuilt. In fact the Russians did not recolonize the area until they built the Great Abatis line, and then successively extended it with the Line Forts in the late 16th/early 17th c.
Besides the Russian cities in Donets basin/Severia/Kiev/Galicia/Zalesye, the Mongols also destroyed Bulgar on the Volga and all its sister cities (also heavily populated places as evidenced by the square footage of the built-up areas), halted the incipient medieval urbanism of the Volga Finns and dispersed them into the forests, and drove away all the Black Sea Cumans (who probably numbered in the hundreds of thousands but maybe short of a million) until they became merely historic minorities in Bulgaria and Hungary; reduced the historically significant Alan kingdom to just one mountain valley population among dozens in the Caucasus; and of course, also wiped out any trace of Russia's Black Hat population (centered on Torchesk and probably quite numerous around Kiev's southern borders).
In fact, Russia-at-large and especially in the south is plunged into a bit of an information vaccuum following the invasions. There are no chronicles, no coins, no written artifacts, nothing, for a whole generation, and only modest examples for over a century later. Almost everything that we know about the period comes from the north, where the cities were either not touched, or else rebuilt quickly by refugees from the South fleeing up beyond the swamps and the protective tree line.
So while it's hard to estimate the precise death toll (simply because it's hard to estimate the actual populations too), the extent of the devastation is hard to overestimate. The Mongols changed everything.
Beyond that, there's a further complication. The Golden Horde itself soon built several major cities, centered on big waterway crossings: one in Moldavia, a few on the Dniepr, a couple on the Don and Donets, lots along the Volga. They were very very large cities and probably housed mostly non-Mongol populations ruled by Mongol and Muslim administrators. If the refugees were herded to build and settle those, maybe the death toll in Russia was a little lighter than estimated.
....of course, it didn't really matter in the end. The Great Discord in the Great Horde disrupted trade and growth only a century into the Mongol rule, and then opened the way for Timur to invade the Great Horde itself.
Every single one of those great Mongol cities on the Volga and Don were burned to the ground. You can imagine what the loss of life is like. The loss of artifacts and historical record doesn't even need any exaggeration. We have a mere handful of any text examples from the Golden Horde period. One of them is a poem fragment. That's all the legacy of a population of several million after Timur dropped by for a visit.
So: tldr; on the lands of modern Russia and Ukraine, the effects of Mongol Invasions Round 1 and Round 2, for both the Rus and their neighbours, were spectacular, devastating, and long-lasting.