To make a new project tab, create a subclass of teamwork:ProjectTabs. If it should show up only for certain project types, use the teamwork:projectTabCondition property with a value such as:
teamwork:getProjectType(?projectGraph) = my:ProjectType
Also note the teamwork:projectTabRole property, which controls the permission required to see the tab. It takes a value such as teamwork:viewer, teamwork:editor, teamwork:manager.
The tabs for working copies (also known as “tags” internally) are more hardcoded, and new working copy tabs cannot be added simply by creating a new class. Instead, the ui:prototype of teamwork:TagPage needs to be overridden (create a clone of teamwork:TagPage, make it a subclass of teamwork:TagPage, have the ui:overrides property of the new class point to teamwork:TagPage, then modify the ui:prototype of the new class). Just add the new tab to the hardcoded list in the prototype.