Manage all part of Azure AD with CSP admin account
With a CSP admin account, not all customer Azure AD features are manageable, despite the fact that you are member of the Global Admin Group in this directory. For instance, when you visit the Access packages page you get the "No Access" error.
Because of this, besides the CSP admin account all administrators also need a customer specific admin account to make management of the full Azure AD possible.
First I thought it was a bug or configuration error, but Microsoft CSP support confirmed this is by design.