Staging site on subdomain – all links dont work except home page

I’d change the first part of your htaccess from

RewriteEngine On
RewriteCond %{HTTP_HOST} !^stagin\.mysite\.com$
RewriteRule ^(.*)$ https://stagin.mysite.com/$1 [R=301,L

to

RewriteEngine On
RewriteCond %{HTTPS} !=on
RewriteRule ^(.*)$ https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301,NE]

This will take any request to any site and force it to SSL. Then the rest of the htaccess will take care of the WordPress stuff.

I think that your first rule is looking for ‘anything not the staging url’ and doing the SSL rewrite. Which means that any staging URL will not be processed (SSL’d), and the WP part will not work properly.