I don't precisely mean React Developer Tools because the UI is unnecessary for this usecase, but it provides similar functionality where you can access the state/props from the component instance.
// resq is the stringified source of the library
// page is a Puppeteer page
// this line injects resq into the page
await page.evaluate(resq);
// This finds a React component with a prop "country" set to "us"
const usProps = await page.evaluate(
`window["resq"].resq$("*", document.querySelector("#__next")).byProps({country: "us"}).props`
);
// This finds a React component with a prop "expandRowByClick" set to true
const news = await page.evaluate(
`window["resq"].resq$("*", document.querySelector("#__next")).byProps({expandRowByClick: true}).props.dataSource`
);