Nginx Wordpress Locking Down WP-Admin and Admin Dashboard

I am trying shut the access the wp-admin with the following codes.

Yes, it works if I go to example.com/wp-admin, I will get blocked. However, if I am signed in as admin and I type example.com/wp-admin/index.php, I still can get in and play around with the dashboard.

Or, I can just simply type example.com/wp-admin/index.php and can still log in from there.

How do I correct this so that there is no access at all on */wp-admin/(whatever)? Except ajax.

Or, is there any method to shut admin dashboard (e.g. from wp setting, etc.)?

Thanks a lot for your time

# Deny brute force access to wp-login.php
location = /wp-login\.php {
    limit_req zone=one burst=1 nodelay;
    fastcgi_pass unix:/var/run/php7.3-fpm.sock;     
}

# Add trailing slash to */wp-admin requests.
rewrite /wp-admin$ $scheme://$host$uri/ permanent;

# Don't cache uris containing the following segments
if ($request_uri ~* "/wp-admin/|/wp-json/|/xmlrpc.php|wp-.*.php|/feed/|index.php|sitemap(_index)?.xml") {
    set $skip_cache 1;
}

# Block wp-admin by IP
location ~* ^/wp-(admin\.php|login\.php|admin/*$|admin/.*\.php) {
    deny all;
    error_page 403 = @wp_admin_ban;
}

location @wp_admin_ban {
    rewrite ^(.*) https://example.com permanent;
}

location /wp-admin/admin-ajax.php {
    allow all;
}