I haven't done this either (yet) but it's my understanding that you can mix them quite easily really.
One of the biggest benefits of using React is that it's a pretty standalone script. You can literally just include it in your site like any other JS scripts and make use of it how you see fit.
Only the stuff that must be "reactive" will communicate over ajax to your own PHP scripts on the server. Or basically, your API.
What you need to do is begin separating your project (PHP side) between directly outputting "pages" versus outputting "data". React just needs the data, it doesn't need PHP pages. So you need to build endpoints on your server which only serve JSON data and handle those API requests.
This means if you have a PHP page being output, let's say for a contact page, you would output the entire page including the React script. This would show up for the user, waiting for their input. And then the user fills in the form and submits it. Well this functionality is perhaps controlled by React. So React sends the form data to the server and waits for the response. On the server side, you have the API handle this request and send back a JSON payload. React then parses the JSON and updates the form with a "thank you" message or whatever. No page reload needed.
The difference is that instead of a PHP page that accepts a POST request and then outputs a result page, you have a PHP script that accepts the POST and outputs just the JSON result data (not a page).
And perhaps you need both? If JS is off and React is broken, the form should submit as normal to a normal PHP script that outputs the normal form result page.
So you've mixed outputting a normal every day PHP page that includes a component controlled with React. The React stuff communicates over ajax back to the server but talks to the PHP API and gets JSON data back, not "pages". React doesn't have to do your routing or render the pages if you don't want it to. And you don't need a Node server to create PHP API endpoints.
This is, again, one of the best features of React that made it so popular. You can stick it just here or there as needed to control just the small "reactive" parts of a page you might need it to. It doesn't have to control the entire page, routing, or rendering. You don't need state management, Node, a Mongo server, or whatever else. It just waits for user events and potentially communicates to the server for some new data. For simple stuff you may not even need JSX.