When you go to the Contacts list, unfortunately, there is no New contact button. And it seems you are locked and cannot extend your Contacts list with new ones.
This unpleasant problem is appearing to you because you have chosen the global Contacts list (all contacts from all projects) via going to Projects (on top) - and then Contacts.
The URL, in this case, will be /contacts
So, to make the New contact button come, you have to .
And the URL now will look like this (it will have the selected project in the path) /projects/[your_project_name]/contacts
Note: This behavior is because the Contacts are project-related and not global by design.