> During the Cold War, you could say "Soviet" instead of "Russian" to clearly demarcate between the nation and the nationality

That's not what that distinguished. It distinguished whether you were talking about things pertaining to the USSR and those specifically having to do with Russia; the same rough difference as between “American” and “Californian” (or, perhaps a better analogy would be “British” and “English”.)

> We don't have a modern equivalent for the PRC

Mostly because China didn't conquer a bunch of neighbors and create a name for the resulting state distinct from “China”, which remains as the name for the absolutely dominant component.

But, again, while the Soviet/Russian distinction did exist, it did not serve the purpose you describe, and we didn't have any linguistic distinction that did.