You have basically started implementing the beginning stages of a front controller, which is commonly used in web based MVC frameworks. Why not just go use a MVC framework already?
This switch case technique is effective until the switch grow beyond half a dozen CASE statements, at which point managing them becomes more work than it’s worth.
Each include is essentially a controller action being dispatched, much like a MVC framework would do for you.
Why use include? I would not use includes personally in that situation. Just call a custom-made functions to do the adding, editing and listing. That would be much neater. One does not have to open different files to check the code.