The "Add new task" button that is built in does add a new task to the task store, that is its purpose. It does not open an editor unless I am mistaken, so that is probably application code? If you want some other behavior in your app, I recommend replacing it with your own button (docs for the column toolbar feature here https://bryntum.com/products/taskboard/docs/api/TaskBoard/feature/ColumnToolbars).
The task edit feature requires a task to exist in the store to have something to edit. If you want to remove it on cancel, you can catch the cancel event on the TaskBoard and handle it there: