Not sure about php include with an URL but could it be that the login process is happening on your webserver "browser" and not your local.
That means you are kind of logged in but not really.
But as I am really not good with PHP this is just a guess.
What happens if you call https://domain.com/a/cgi/page.cgi?p=dynamic-test direcly from your browser?
Do you check the session within your PHP script?

Regards

n||i||k||o