The problem is that most Circassians went to Muslim countries and I am sorry to be blunt, but the Muslim countries were far behind the West for much the 20th century.
Perhaps it is worth considering not an independent Circassia but a timeline where Russian government invites them to return to their homeland. England kicked out its own Jews but let them return eventually. Circassia might get autonomy under Russian sovereignty but not independence. That might be a deal breaker to many Circassians but would it be good enough for half or a quarter of the diaspora to return? That is still a couple million people. It depends on the conditions I suppose. We need to factor: what is the Russian Government like, what terms is it willing to offer, and how would the diaspora respond.
The Tsarist Government strikes me as the least likely. There was policy of slow but steady Russification throughout the Empire and I doubt the any Circassicans would want to return to their homeland while the same regime that had committed horrors on them would still rule it.
The Soviet Union could create a Circassian SSR like it did in the southern Caucasus and promise autonomy. However State Atheism might be a turn away many Circassicans. Plus, a Circassian SSR does increase the chances of independence if the USSR falls apart like in OTL.
Than we have a Russian Republic. What would they do? Lots of unknowns here. They won't be state atheist might be willing to guarantee freedom of language, speech, and religion. The more liberal the government is the more they might be willing to offer but a Russian Republic would change things far beyond Circassia. Republican Russia timelines are uncommon on this site. I can understand why, they take a lot of study to do well.