However, the Mongolians weren’t able to change the language of the locals of Moscow.

They didn't try. Generally, the Mongols were much more likely to adopt the language of the locals, rather than the locals adopt Mongolian. For example, urban Persian remained Persian-speaking, and rural Persian remained Persian-speaking or Turkic-speaking, as they had been before. China kept speaking Chinese languages, Korea remained Korean-speaking. Armenia and Georgia kept their languages.

Further, where the descendants of Mongol rulers remained in power for a long time, in non-Mongolian-speaking regions, they adopted the local languages. The Golden Horde rulers adopted Turkic, and the Chagatai Khanate adopted Turkic. Notably, the Golden Horde is often called the "Kipchak Khanate", as the main group in the population were Kipchak Turks.

Second, the number of Mongols in Moscow would have been very small. At the time of the Mongol conquest, Moscow wasn't even the most important town/city in the principality of Vladimir - Vladimir and Suzdal were the main cities, and at best Moscow would have been third after them. As can easily be the case with predominantly wooden towns/cities, Moscow, and Vladimir and Suzdal, were burned during the conquest. As can also easily be the case, these cities were rebuilt.

The Mongols placed military and civilian governors in the major cities: Kiev, Bulgar (the capital of Volga Bulgaria), and "Asud" and "Sesud". These last two cities haven't been identified with certainty, but might be Tana/Ornas/Azov (at the mouth of the Don) and Saksin (in the Volga delta). Of these, only Kiev was in Rus' lands. By the mid-14th century, the military governors were gone, and the civilian governors lived in Sarai, the main city of the Golden Horde. (The Russian chronicles refer to these governors by their Turkic titles, baskak and daruga, rather than by their Mongolian titles (tamma/tammachi and darugha/darughachi).)

With no Mongol governor or Mongol administration in Moscow, no occupying Mongol forces in Moscow, and no pressure from the Mongols to adopt Mongolian as a language, it's easy to see why Moscow remained Russian-speaking.

Even though most historians are familiar with the Mongolian invasion, very few people like me, were even familiar with the Slavicization of Moscow in 950 AD. Therefore, I’m deducing that the Mongolian invasion was much more newsworthy than the Slavic migrations of 950 AD.

We don't know how newsworthy the Slavicisation of Moscow was - this was before widespread literacy in Russian lands, and news was oral. We have essentially no contemporary sources describing this event or process. Moscow itself only enters history about 200 years later, first mentioned in chronicles in the mid-12th century. Moscow not being a major city during the Mongol conquest, there is very little mention of it then, either. There are probable references to its destruction in Mongol and Chinese sources (with some uncertainty as to exactly which cities are meant in these sources - names that have been Sinicised from Mongolised names (possible via Turkified names) often bear little obvious relation to the original Russian names).

With the Slavic settlement of Moscow in what is essentially Russian prehistory, and the Mongol conquest being historical, and of great importance for the history of Moscow, and of much greater interest to historians outside the field of Russian history, it should be no surprise to see it better known. For an English analogy, we know far more about the Norman conquest of England than we know about the early arrivals of Angles, Saxons, and Jutes in England, and people are much more aware of the details.

(The Mongol conquest of the Russian lands helped the growth of Moscow a lot. First, it destroyed the powerful Russian cities like Kiev. Second, Moscow was able to grab the title of Prince of Vladimir for some time (being friendly with the Khan of the Golden Horde, and also being married to his sister, helped) allowed them to control the Church (and move its administration to Moscow) and to become the official tax-collectors in the area (the tax collection was for the Mongols, but tax collectors were typically adept at collecting a little (or not-so-little) extra for themselves).