For a comparison the Kuznetsov is carrying 3 Mig-29K and maybe twice as many Su-33 [1]. And here's what a USN CVN looks like on its way to deployment [2]. I'm too lazy to count the aircraft.
While it looks like the Kuznetsov may be capable of carrying twice as many aircraft as pictured, that's the equivalent of one helicopter squadron and one mixed attack/air superiority squadron. Then again, there's a reasonable assumption that Russia's main force projection is due to how much of the populated world is nearly immediately accessible via Russian-controlled land bases, with much less need for force projection across oceans compared to the US.
Though they dropped one of the MiG-29s in the ocean a couple of days ago...
But that's still a magnitude more powerful than what most second / third-tier countries can summon from their entire armed forces. For example in Africa, perhaps only Algeria, Morocco, Angola and South Africa would have any hope of taking-on such a force, and that's not even considering the carrier's escorts.
After all, whenever there's a world event, one of the first questions asked by the United States leadership is, "Where is the nearest carrier group?"
There is no longer a unipolar hegemony in Eurasia. That's the message these maneuvers, and indeed the Chinese acquisition of this carrier itself, are intended to convey.