nginx how to remove index.php from URL for an MSM site?

I have an existing Expressionengine MSM site that I've moved to nginx on my local machine, consisting of 2 sites in subdirectories:

/en
    /system
    /index.php
    /admin.php
/de
    /index.php
    /admin.php
/themes

Sites are accessed through https://mydomain.test/en and https://mydomain.test/de

I can view pages using 'index.php' : https://mydomain.test/en/index.php?/pagename

But I can't seem to get the site working without 'index.php?', my nginx.conf is included below (https://www.nginx.com/resources/wiki/start/topics/recipes/expressionengine/)

user username staff;
worker_processes auto;

events {
    worker_connections  1024;
}

worker_rlimit_nofile 1024;

http {
    include mime.types;
    default_type  application/octet-stream;

    sendfile on;
    keepalive_timeout  65;
    client_max_body_size 128M;

    gzip  on;
    gzip_comp_level 5;
    gzip_min_length 256;
    gzip_proxied any;
    gzip_vary on;

    gzip_types
    application/atom+xml
    application/javascript
    application/json
    application/rss+xml
    application/vnd.ms-fontobject
    application/x-font-ttf
    application/x-web-app-manifest+json
    application/xhtml+xml
    application/xml
    font/opentype
    image/svg+xml
    image/x-icon
    text/css
    text/plain
    text/x-component;

    include /Users/username/.valet/Nginx/*;
    include servers/*;
    include valet/valet.conf;

    server {
        listen 80;
        server_name mydomain;
        root /Users/username/nginx/mydomain/;
        index index.php;

        access_log /usr/local/var/log/nginx/access.log;
        error_log  /usr/local/var/log/nginx/error.log info;

        location /en {
           try_files /en/$uri /en/$uri/ /en/index.php?$query_string;
           disable_symlinks off;
        }

        location /de {
           try_files /de/$uri /de/$uri/ /de/index.php?$query_string;
           disable_symlinks off;
        }

        location @ee {
            rewrite ^(.*) /index.php$1 last;
        }

        location ~ \.php$ {
            include fastcgi_params;
            fastcgi_pass unix:/tmp/php-fastcgi.socket;
            fastcgi_index index.php;
            fastcgi_param SCRIPT_FILENAME 
            $document_root$fastcgi_script_name;
        }

        # This location is for our EE index.php gateway
        location /index.php {
            include /usr/local/etc/nginx/fastcgi_params;
            set $script     $uri;
            set $path_info  $uri;
            # this will set the path_info when it exists as query string: /index.php?/something/here
            if ($args ~* "^(/.+)$") {
                set $path_info  $1;
            }
            fastcgi_pass 127.0.0.1:9000;
            fastcgi_index index.php;
            fastcgi_param SCRIPT_FILENAME 
            $document_root$fastcgi_script_name;
            fastcgi_param PATH_INFO $path_info;
        }
    }

}