Wordpress redirect rules in WP-engine for wp-admin

Question

I have my WordPress site hosted in Wp-Engine. The Url for the site is https://www.example.com/blogs. I have another AEM site at https://www.example.com. I have the following Web Rules in Wp-Engine for redirection.

1. Internal rewrite /blogs/(.*) /$1

2. Permanent redirect (301 status code) `/blogs https://www.example.com/blogs`

Now I have the following issues.

1. I am not able to access https://www.example.com/blogs/wp-admin directly. It is going to https://www.example.com/404.html. But I can access https://www.example.com/blogs/edit.php or https://www.example.com/blogs/plugins.php

2. When I perform a search on Posts or Users, I am redirected to https://www.example.com/wp-admin/edit.php?s=dummy&post_status=all&post_type=post&action=-1&m=0&cat=0&layout=63bff7d64f656&paged=1&action2=-1

Note there are no /blogs added, so it is looking into the AEM site for the page, and as it is not there, it is again a 404 page.

I have added the following rule, but it is also not working.

Permanent redirect (301 status code) /wp-admin/(.*) http://www.example.com/blogs/$1

It would be very helpful if someone could point me in the right direction.

Update: It seems like the issue is when there is a query string in the URI. There is a 302 redirect, which cuts the blogs part from the URL