Reconcile differences between "TreeEditor_demo" and "tree_editor"

The `"TreeEditor_demo"` contributed by the traitsui package to the etsdemo application has a lot in common with the documentation example `"tree_editor"`. The documentation example is included in the standard trait editors page - and once the differences have been reconciled, we can remove the latter from the codebase entirely. We can potentially also remove the literalinclude from the documentation page at that point, decluttering it in the process.

Ref https://github.com/enthought/traitsui/pull/1640