How to add tabs to panels setting page?
Those vertical items are internally called "operations" and are implemented by task_handlers plugins although some of them are hardcoded in page_manager. You can see some examples in:

ctools/page_manager/plugins/task_handlers/http_response.inc 
panels/plugins/task_handlers/panel_context.inc


You may also find more info in page_manager_render_operations()  docstrings.