Apache/Nginx - some web server will be used, though much as likely something more lightweight than Apache. No proxy_pass needed since Gatsby just generates a bunch of files you need to serve
MySQL - probably not unless married with a very complex backend
PHP - yeah that’s out
To understand Gatsby it’s crucial to understand that it’s using a significantly different architecture than traditional LAMP applications and monolithic CMSes
Just about every production Gatsby instance is either using static data source (list of markdown/json files) or a monolithic CMS on the backend via API. It's more of a modern frontend site framework rather than a true self-contained app.
Apache - Gatsby doesn't run behind a load balancer (apache/nginx) with proxy_pass?
MySql - Gatsby doesn't persist data into a database (MySql/Postgres)?
PHP - I'll give you that PHP is out and node.js is in for backend development.