It kinda depends on which version you're using. So as an example from my deployment, if I'm using experience Builder right from the app launcher in my Enterprise Portal (10.8.1) I do not have access to the search widget:
But, if I use the developer edition which I just upgraded to the newest version (very similar to AGOL), I do have access to it:
If you want to give the developer edition a crack, I think it's kinda nice, but that depends on if you have a web server or not.