Best way to add mobile CSS on an existing webpage designed with react?

I want to add a responsive design to my already built web application. Is it my best approach to detect dimension at top level component and conditionally render different component base on users on desktop or mobile ?

I've design responsive website by only css, or with a framework like tailwind in the past, but refactoring an existing application that has elements style tied to logic impose a challenge to do with css alone.