I know there's a debate around Mandarin's level of influence from the Turko-Mongol-Manchu languages, but modern Standard Mandarin is based on the variety spoken in Beijing. Beijing became the capital only during the Yuan, and the ROC standardized the national language around it only because it was the official language of the Qing. The Ming played an important role here too, to be fair, but the reason the Ming moved their capital to Beijing also had to do with the Yuan.A cursory look at the actual Mongol, Jurchen, Khitan and Manchu languages makes it clear that none of them sound anything close to Mandarin. None of them are tonal or have monosyllabic morphemes and only Manchu is limited to -vowel and -n/ng endings.
Mandarin evolved because Middle Chinese was changing in the Song dynasty and got too complicated so sounds and tones got merged. It had nothing to do with Mongol, Jurchen, Khitan or Manchu influence. If it did, where are the Mongol, Jurchen, Khitan or Manchu loanwords? Mandarin has more Indian loanwords than all of those combined (yes I know, Jai Hind) and I don't know a single common loanword from any of those languages. In contrast, an actual conquered language like English has like 50% French and Latin vocabulary due to Norman French kings conquering the Anglos.
We also have proof of the natural emergence of Mandarin in the late Song early Yuan era with 中原音韵 which showed how people talked in 1200-1300. The scholars compiling this book even said they realized that how people talked has deviated substantially from the days of 广韵 (1000 AD) and even further from 切韵 (600 AD). The time distance from 切韵 to 中原音韵 is the distance from Anglo-Saxon (800 AD) to barely recognizable modern English (1500 AD). The time distance from 广韵 to 中原音韵 is the distance from Shakespeare to 1950's English. Yet 中原音韵 is already close to modern Mandarin. You'd also note that 中原音韵 is only a few years after the Mongols, far before the Manchus, and in a region far away from the Khitans.
What I'm saying is, if these conquests did not happen, based on Tang and Song trends, the official language of China would've likely been either not Mandarin, or at least not Beijing Mandarin. Neither of those dynasties had their capitals any where near Beijing, and for the Tang, at the minimum, we knew their court language was more similar to Cantonese. So it wouldn't have been Beijing Mandarin that became the standard.