To answer that last question, it's because WAB is built on the ArcGIS JS 3.x API, which is in the process of being phased out in favor of tools built on the 4.x API. You can think of EB as not so much an alternative to WAB as the 4.x version of it.
That said, EB is very different in how widgets interact, particularly because EB allows from any number of different maps (including none!) to be added to the same experience. To get things like the Search widget to "talk" to your other widgets like maps and lists, you need to add triggers. For instance, I have a search widget that, upon selecting a record from the search results, will automatically send a "Zoom to" message to my Map widget.
I can easily set additional triggers to apply to other maps, or non-spatial widgets.
I don't have any useful information about the Print widget, except that it's supposed to be on the roadmap for the "near term" 2022. We've just been giving our users a tutorial of how to take screenshots on their computer, and that seems to have alleviated some of the "print the map" requests for the time being.
- Josh Carlson
Kendall County GIS