`wp-admin` not working when serving Laravel and WordPress from different folders using NGINX

I am using the below NGINX configuration to serve a Laravel application and a WordPress blog. The blog used to be in a sub-domain (blog.example.com), but now moving to example.com/blog.

I am trying to separate both the Laravel application (/var/www/vhosts/example.com/httpdocs/laravel/public) and the WordPress (/var/www/vhosts/example.com/httpdocs/wordpress/) installations into different folders so it is easy to manage. The Laravel routes are working as expected, but the WordPress example.com/blog/wp-admin route is not working. Below is my NGINX configuration.

server {
    listen 80;
    server_name example.com;
    rewrite ^/(.*) https://example.com/$1 permanent;
}

server {
    listen 443 ssl;
    server_name example.com;

    charset utf-8;

    ssl    on;
    ssl_certificate     /etc/ssl/example.crt;
    ssl_certificate_key /etc/ssl/example.key;

    root /var/www/vhosts/example.com/httpdocs/laravel/public;
    index index.html index.htm index.php;

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

    location = /favicon.ico { access_log off; log_not_found off; }
    location = /robots.txt  { access_log off; log_not_found off; }

    error_page 403 /index.php;
    error_page 404 /index.php;

    location ~ .php$ {
        fastcgi_split_path_info ^(.+.php)(/.+)$;
        fastcgi_pass unix:/var/run/php/php7.4-fpm.sock;
        fastcgi_index index.php;
        fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
        fastcgi_read_timeout 180;
        include fastcgi_params;
    }

    ## WordPress blog configuration
    location ^~ /blog/ {
        alias  /var/www/vhosts/example.com/httpdocs/wordpress/;

         if (!-e $request_filename) {
            rewrite ^ /blog/index.php last;
        }

        try_files $uri $uri/ /blog/index.php;

        location ~ .php$ {
            fastcgi_split_path_info ^(/blog)(/.*)$;
            fastcgi_pass unix:/var/run/php/php7.4-fpm.sock;
            fastcgi_index index.php;
            fastcgi_param SCRIPT_FILENAME $request_filename;
            fastcgi_read_timeout 180;
            include fastcgi_params;
         }
    }

    location ~ /.(?!well-known).* {
        deny all;
    }
}

Please could you point me, why I am unable to access wp-admin? Is there a better way to do this? Thanks