Access non-WP site cookie that is on subdomain

I’m creating an eCommerce site with WordPress as the front end on the primary domain “www.domain.com”, and the eCommerce platform (called CommerceV3) on a subdomain “shop.domain.com”. Is there a way for WP to access cookie info from the subdomain to tell if a user is logged in on the eCommerce side? I simply want to display a dynamic “Login” or “Logout” link in WP, depending on the users authentication status on the eCommerce side.

Thanks!