LightBarControllerImpl.Factory: call start to keep legacy behavior

Before, LightBarControllerImpl was doing work in the constructor, which
moved to start().
To keep the same behavior as before in the legacy path (NavigationBar),
we need to manually call start().

Test: Manual - Build & Run and make sure LightBarControllerImpl is
      behaving as expected.
Flag: EXEMPT simple fix
Bug: 379344858
Change-Id: I892c61a05c4c8c1547eddfc70bbdc28688d6490f