Extend UITester support for DateEditor

The goal would be to extend support for downstream projects to write tests that require interacting with the GUI objects created by DateEditor.

Actions:
(1) Look into existing tests for the editor and decide if any of the interactions are going to be useful downstream.
(2) Add more tests for the editor with any new interactions that are going to be useful in downstream code as well.
(3) Expand the testing support via the default target registry used by UITester.
(4) Convert the existing tests for the editor to use UITester.

Optional and opportunistic: See if a test can be added for the demo using this editor (if there is one), related to #1257. It might also provide motivation as to what features are likely useful downstream.