Enable Note Task Widget Shortcut

* Enable shortcut feature.
* Enable unit and integration tests.
* The shortcut has been disabled due to b/316332684.
* The integration tests have been disabled due to b/316553495.
* For more context, see ag/25657910 and ag/25692651.

Test: atest NoteTaskControllerTest
Flag: NONE
Fix: b/317010838
Change-Id: I9bee8b0da77d40bcc4a03a4d4201d6b73efbb14b