How to create a menu navigation on a Views page that uses contextual filters?
Open the view where you had created the pages at projects/%/details or projects/%/people.

Under page settings where you had the path filled, add these additional settings to create a Menu tab or a Contextual link.

Go to Menu and select Menu tab as the type and fill in the title. If you want the link to be present as a contextual link, check the box which says context.

You can also set access permissions on who can see this tab depending upon the permission type you had selected.