Description
The thing that at least on Marshmallow is available to set at Android Settings -> Apps -> Gear icon -> Default apps -> Assistant & Voice input -> Assist app.
In Fennec this was added as a low key replacement for the search widget/stand-alone search activity, and long-pressing the home button simply opens a new tab with the input focus in the URL bar.
In theory it might also be interesting to try implementing the actual Assist App API that was introduced with Marshmallow, e.g. to try finding out whether some text is currently selected in an app and then offer starting a search with that text.
But I've got no idea whether that possible, and if yes, how much effort it would be, so having the current Fennec behaviour would be enough as a starting point.