403 Forbidden when trying to reach my simple test page

Your config is intentionally blocking it:

location ~ /. {
    access_log off;
    log_not_found off;
    deny all;
}

That'll match any request where a slash is followed by a character of any kind; the . character in a regular expression means "any character".

I'm assuming you meant to check for a literal .; that'd be this config:

location ~ /\. {

Let me know if that's not the case!