The Playwright library exposes its API through `Browser`, `BrowserContext`, and `Page` objects, which can be used to control different parts of the browser. These concepts enable developers to isolate shared resources such as cache, cookies, and history between multiple contexts and pages. Leveraging `BrowserContexts` is beneficial for parallelization and cookie management tasks, while `Pages` are useful for granular control over navigation and history. By reusing `BrowserContext` instances across multiple sessions using Browserbase, developers can persist authentication flows and support custom Chrome Extensions, ensuring better performance.