WordPress multisite second site admin resulting in too many redirects error

There seems to be some issue the the nginx config. Is there any reason you have modified this rule differently then as documented in the wordpress documentation ? (https://wordpress.org/support/article/nginx/#wordpress-multisite-subdirectory-rules)

I am specifically talking about following rule :

if (!-e $request_filename) {
 rewrite /wp-admin$ $scheme://$host$uri/ permanent;     
 rewrite /wp-admin$ $host/$uri/ permanent;
 rewrite ^(/[^/]+)?(/wp-.*) $2 last;
 rewrite ^(/[^/]+)?(/.*.php) $2 last; 
}

I think you can remove the 3rd line in the above rule ( rewrite /wp-admin$ $host/$uri/ permanent; ) as it’s not there in the documentation too .. and I think all needed is already there in the first rule of this block.

Beside that in the last rule (rewrite ^(/[^/]+)?(/.*.php) $2 last;) is missing an escape sequence, which is also present in the documentation.
So Can you try replacing the above block completely as present in the document like shown below ?

if (!-e $request_filename) {
        rewrite /wp-admin$ $scheme://$host$request_uri/ permanent;
        rewrite ^(/[^/]+)?(/wp-.*) $2 last;
        rewrite ^(/[^/]+)?(/.*\.php) $2 last;
    }