ESP8266WebServer how to parse Json payload in post request that is bigger than the ram
The ESP8266WebServer library can process only a HTML-Form POST request of application/x-www-form-urlencoded or mulripart/ content type.

You could sent the JSON as multipart 'upload' to save it to file, but it would require to build the multipart format of the POST body.

If you want to process POST with application/json content type, you could make a simple web server implemented with WiFiServer.