Oh, my bad, I misread the issue, sorry about that.
So the issue is you’re rewriting all requests to /index.php, including JS, CSS and image assets. So those fail to load with file_server.
You’ll basically have to only rewrite requests that don’t map to files that already exist on disk. To do this, you can use the file matcher.
Also, please review the docs for php_fastcgi, in particular the Expanded Form section which explains how it works: