Is there a way to tell or are we going by what these companies disclose?
Use the react devtools when looking at those websites.
And also Office 356
Both Airbnb and O365 web apps are horribly slow in the browser and hasn't had any noticeable feature growth in the past 4 years so i wouldn't use these as good examples of neither performance nor productivity.
Isn't a good chunk of AirBnB, Facebook, Instagram, Netflix, The New York Times and Dropbox written in React?
The built-in state management has limitations, of course. I see it best for keeping state relevant to display-- React is supposed to be a "view" library, not a state management one.