> Russian Empire didn't give the conquered nations the alphabet, but USSR did, as part of supporting local nationalists.

Many languages of Russia got their alphabets already in the late nineteenth century or around the 1906 rebellion. If you look at publications then in Mari, Chuvash, Ossetic, etc. the Cyrillic orthography already has most of the special characters that were used in the Soviet era. (Moreover, many of these languages never had a Latin-alphabet phase.)

But in the USSR, official doctrine required crediting the Bolsheviks with the development of minority-language writing, and it became taboo to mention all the pre-1917 developments. Only around the time of glasnost and perestroika was this era revisited in Soviet scholarship, but many ordinary Russians remained unaware they had been taught a myth.

Your claims elsewhere here about Uzbek are out of date. I have traveled extensively in UZ and, as an OSM mapper, I am constantly looking at signage. There is exceedingly little Cyrillic left in most of the country. So little that when one spots it, it seems a bit of a novelty.