I just got this bug logged, and I'd love to see Esri fix it: BUG-000171971
"Setting the label property on the search widget simply does not change/update the default aria-label."
If you'd like details, just read the comments in this codepen: https://codepen.io/Mike-Dolbow/pen/eYqvRZd and then see the workaround in another pen: https://codepen.io/Mike-Dolbow/pen/MWNpvQX
Not only is this a "documentation is incorrect" issue, but it's a pretty serious accessibility issue. Since the widget can be customized to search a variety of sources, the simple default aria-label of "Search" is woefully inadequate, even for the default sources. The ability to customize it is pretty critical.
Hoping I can get some upvotes on this to escalate it and get it fixed in a future version.