How to log into Sophos Central directly?

Try: https://central.sophos.com/manage/partner/dashboard 

Thanks! It works!

And what's the central URL for the administrator of our customer to manage their products?

Is https://central.sophos.com/manage/overview/dashboard the right address for them?

Thanks! It works!

And what's the central URL for the administrator of our customer to manage their products?

Is https://central.sophos.com/manage/overview/dashboard the right address for them?

If your customers have admin accounts created directly on the sub-estates for their sites, they can log in using "cloud.sophos.com" or "central.sophos.com" directly. 

It is only the Partner Portal login which behaves slightly differently. The link you posted will also work.