Correcting 404 Error with modified_nginx.conf.sample

When trying to access my magento site I keep getting 404 errors and running

sudo tail /var/log/nginx/error.log

I see the following:

2023/10/19 20:26:32 [warn] 318594#318594: *166 using uninitialized "mage_root" variable, client: x.xx.xxx.xx, server: example.com, request: "GET /subdirectory/ HTTP/1.1", host: "example.com"
2023/10/19 20:26:32 [error] 318594#318594: *166 open() "/var/www/example.com404" failed (2: No such file or directory), client: x.xx.xxx.xx, server: example.com, request: "GET /subdirectory/ HTTP/1.1", host: "example.com"

I initially had errors where I could not get the nginx.conf.sample to work

but that was resolved using the information from that question now I am wondering was there an
additional change that need to be made to address this error.

Here is the modified nginx conf:

## Example configuration:
# upstream fastcgi_backend {
#    # use tcp connection
#    # server  127.0.0.1:9000;
#    # or socket
#    server   unix:/var/run/php/php7.4-fpm.sock;
# }
# server {
#    listen 80;
#    server_name mage.dev;
#    set $MAGE_ROOT /var/www/magento2;
#    set $MAGE_DEBUG_SHOW_ARGS 0;
#    include /vagrant/magento2/nginx.conf.sample;
# }
#
## Optional override of deployment mode. We recommend you use the
## command 'bin/magento deploy:mode:set' to switch modes instead.
##
## set $MAGE_MODE default; # or production or developer
##
## If you set MAGE_MODE in server config, you must pass the variable into the
## PHP entry point blocks, which are indicated below. You can pass
## it in using:
##
## fastcgi_param  MAGE_MODE $MAGE_MODE;
##
## In production mode, you should uncomment the 'expires' directive in the /static/ location block

# Modules can be loaded only at the very beginning of the Nginx config file, please move the line below to the main config file
# load_module /etc/nginx/modules/ngx_http_image_filter_module.so;

root $MAGE_ROOT/pub;

index index.php;
autoindex off;
charset UTF-8;
error_page 404 403 = /errors/404.php;
#add_header "X-UA-Compatible" "IE=Edge";


# Deny access to sensitive files
location ~ ^/subdirectory/.user.ini {
    deny all;
}

# PHP entry point for setup application
location ~* ^/setup($|/) {
    root $MAGE_ROOT;
    location ~ ^/setup/index.php {
        fastcgi_pass   fastcgi_backend;

        fastcgi_param  PHP_FLAG  "session.auto_start=off n suhosin.session.cryptua=off";
        fastcgi_param  PHP_VALUE "memory_limit=756M n max_execution_time=600";
        fastcgi_read_timeout 600s;
        fastcgi_connect_timeout 600s;

        fastcgi_index  index.php;
        fastcgi_param  SCRIPT_FILENAME  $document_root$fastcgi_script_name;
        include        fastcgi_params;
    }

    location ~ ^/setup/(?!pub/). {
        deny all;
    }

    location ~ ^/setup/pub/ {
        add_header X-Frame-Options "SAMEORIGIN";
    }
}

# PHP entry point for update application
location ~* ^/update($|/) {
    root $MAGE_ROOT;

    location ~ ^/update/index.php {
        fastcgi_split_path_info ^(/update/index.php)(/.+)$;
        fastcgi_pass   fastcgi_backend;
        fastcgi_index  index.php;
        fastcgi_param  SCRIPT_FILENAME  $document_root$fastcgi_script_name;
        fastcgi_param  PATH_INFO        $fastcgi_path_info;
        include        fastcgi_params;
    }

    # Deny everything but index.php
    location ~ ^/update/(?!pub/). {
        deny all;
    }

    location ~ ^/update/pub/ {
        add_header X-Frame-Options "SAMEORIGIN";
    }
}

location ~ ^/subdirectory/ {
    try_files $uri $uri/ /index.php$is_args$args;
}

location ~ ^/subdirectory/pub/ {
    location ~ ^/pub/media/(downloadable|customer|import|custom_options|theme_customization/.*.xml) {
        deny all;
    }
    alias $MAGE_ROOT/pub/;
    add_header X-Frame-Options "SAMEORIGIN";
}

location ~ ^/subdirectory/static/ {
    # Uncomment the following line in production mode
    # expires max;

    # Remove signature of the static files that is used to overcome the browser cache
    location ~ ^/static/versiond*/ {
        rewrite ^/static/versiond*/(.*)$ /static/$1 last;
    }

    location ~* .(ico|jpg|jpeg|png|gif|svg|svgz|webp|avif|avifs|js|css|eot|ttf|otf|woff|woff2|html|json|webmanifest)$ {
        add_header Cache-Control "public";
        add_header X-Frame-Options "SAMEORIGIN";
        expires +1y;

        if (!-f $request_filename) {
            rewrite ^/static/(versiond*/)?(.*)$ /static.php?resource=$2 last;
        }
    }
    location ~* .(zip|gz|gzip|bz2|csv|xml)$ {
        add_header Cache-Control "no-store";
        add_header X-Frame-Options "SAMEORIGIN";
        expires    off;

        if (!-f $request_filename) {
           rewrite ^/static/(versiond*/)?(.*)$ /static.php?resource=$2 last;
        }
    }
    if (!-f $request_filename) {
        rewrite ^/static/(versiond*/)?(.*)$ /static.php?resource=$2 last;
    }
    add_header X-Frame-Options "SAMEORIGIN";
}

location ~ ^/subdirectory/media/ {

## The following section allows to offload image resizing from Magento instance to the Nginx.
## Catalog image URL format should be set accordingly.
## See https://docs.magento.com/user-guide/configuration/general/web.html#url-options
#   location ~* ^/media/catalog/.* {
#
#       # Replace placeholders and uncomment the line below to serve product images from public S3
#       # See examples of S3 authentication at https://github.com/anomalizer/ngx_aws_auth
#       # resolver 8.8.8.8;
#       # proxy_pass https://<bucket-name>.<region-name>.amazonaws.com;
#
#       set $width "-";
#       set $height "-";
#       if ($arg_width != '') {
#           set $width $arg_width;
#       }
#       if ($arg_height != '') {
#           set $height $arg_height;
#       }
#       image_filter resize $width $height;
#       image_filter_jpeg_quality 90;
#   }

    try_files $uri $uri/ /get.php$is_args$args;

    location ~ ^/media/theme_customization/.*.xml {
        deny all;
    }

    location ~* .(ico|jpg|jpeg|png|gif|svg|svgz|webp|avif|avifs|js|css|eot|ttf|otf|woff|woff2)$ {
        add_header Cache-Control "public";
        add_header X-Frame-Options "SAMEORIGIN";
        expires +1y;
        try_files $uri $uri/ /get.php$is_args$args;
    }
    location ~* .(zip|gz|gzip|bz2|csv|xml)$ {
        add_header Cache-Control "no-store";
        add_header X-Frame-Options "SAMEORIGIN";
        expires    off;
        try_files $uri $uri/ /get.php$is_args$args;
    }
    add_header X-Frame-Options "SAMEORIGIN";
}

location ~ ^/subdirectory/media/customer/ {
    deny all;
}

location ~ ^/subdirectory/media/downloadable/ {
    deny all;
}

location ~ ^/subdirectory/media/import/ {
    deny all;
}

location ~ ^/subdirectory/media/custom_options/ {
    deny all;
}

location ~ ^/subdirectory/errors/ {
    location ~* .xml$ {
        deny all;
    }
}

# PHP entry point for main application
location ~ ^/(index|get|static|errors/report|errors/404|errors/503|health_check).php$ {
    try_files $uri =404;
    fastcgi_pass   fastcgi_backend;
    fastcgi_buffers 16 16k;
    fastcgi_buffer_size 32k;

    fastcgi_param  PHP_FLAG  "session.auto_start=off n suhosin.session.cryptua=off";
    fastcgi_param  PHP_VALUE "memory_limit=756M n max_execution_time=18000";
    fastcgi_read_timeout 600s;
    fastcgi_connect_timeout 600s;

    fastcgi_index  index.php;
    fastcgi_param  SCRIPT_FILENAME  $document_root$fastcgi_script_name;
    include        fastcgi_params;
}

gzip on;
gzip_disable "msie6";

gzip_comp_level 6;
gzip_min_length 1100;
gzip_buffers 16 8k;
gzip_proxied any;
gzip_types
    text/plain
    text/css
    text/js
    text/xml
    text/javascript
    application/javascript
    application/x-javascript
    application/json
    application/xml
    application/xml+rss
    image/svg+xml;
gzip_vary on;

# Banned locations (only reached if the earlier PHP entry point regexes don't match)
location ~* (.php$|.phtml$|.htaccess$|.htpasswd$|.git) {
    deny all;
}

with the following in the main Nginx server configuration

location ^~ /subdirectory/ {
    set $MAGE_ROOT /var/www/example.com/subdirectory;
    include /var/www/example.com/subdirectory/custom_nginx.conf;
} 

I am thinking it has something to do with line 37

error_page 404 403 = /errors/404.php;

I tried

error_page 404 403 = ~ ^/subdirectory/errors/404.php;
# or
error_page 404 403 = ~ ^/errors/404.php;

but that results in

nginx: [emerg] invalid value "=" in /var/www/example.com/subdirectory/modified_nginx.conf:37

failing so I am at a loss as to how to correct this error.