I’m aware that the Tatars were remnants of Genghis Khan’s Mongol Empire and that they spent decades preying on the Russian Principalities but how did they all die? Because I feel like they did not last for that long. Did Russia conquer them all? Were they destroyed by rebels? Did something else I’m not aware of happen to them? What was their fates?
I wrote an answer on the history and idea of Tatars a few months ago, that might be of interest.
The rough idea is that a Chingissid state called the "Golden Horde" , which in turn broke up into a number of successor states, that were conquered by Muscovy/Russia in the 16th-18th centuries.
But Tatar people didn't "all die". There are still millions of ethnic Tatars! There are a number of different Tatar communities, the largest being the community in Russia that largely lives along the Volga River near the city of Kazan. Volga Tatars are the second-largest ethnic group in Russia after ethnic Russians, and have their own autonomous republic known as Tatarstan.
Another significant community of Tatars lives in Crimea, currently under Russian control. Large numbers of this community emigrated to Anatolia in the 19th century, when they stopped being a majority of the population, and the whole community was deported to Central Asia by the Soviet government in 1944 (they were allowed to return in 1991).
There are smaller communities of Tatars in Siberia, and in Poland-Lithuania, the latter known as "Lipka Tatars". This group is mostly assimilated into the local population (although some remain practicing Muslims), but have played a role in Polish history, notably aiding in the Polish defense of Vienna against the Ottomans in 1683. Some more famous people of Polish heritage who have Lipka Tatar ancestry include Charles Bronson and Martha Stewart.
Many make a mistake by putting an equal sign between the Tatars and the Mongols. We have not only different languages (Tatars belong to the Turkic group and are therefore closer to Turks or Uzbeks), but also the origin itself. Tatars went from the Turkic people of the Bulgars, and the Mongols have a completely different ethnogenesis.
Tatars themselves suffered from the Mongols as well as the Russians. The ancient city of Bulgar was destroyed by the Mongol conquerors, and its inhabitants conquered. But later, due to the small number of Mongols, they assimilated with the local Türks and formed khanates like the Golden Horde, which had some of the attributes even from the Mongols and where Genghisides ruled, that is, descendants of Genghis Khan. And initially it, and then other khanates on its land, kept Russian principalities and surrounding peoples at bay, but over time they weakened due to internal unrest, which resulted in the conquest of Muscovy (I personally hold the view that Russia essentially became the heir Golden Horde and other khanates, as she subjugated all the former khanates and headed for a similar policy.)
What happened to the Turkic peoples conquered by the empire of Russia? They still live, some got freedom, some, I hope, will get it in the future.