How to enable changing the status of my own Element Type
That's because those buttons are ActionButtons and they have actually nothing to do with statuses in general since the status is not a single field value nor is there a value in the DB that's called status. For example: the status of an entry depends on several different attributes like expiryDate or the date when it's published so there is no way to set those statuses via button there.

You'll need to register the action buttons for your element type. Just take a look at an entries defineActions function.