How do I access that feature?
Somebody has to code it. Search will be simple, that "should" just need code to enable it as its built in to GTK. But if you start at the top and start typing a filename the selected item in the documents list should go to that file on `enter`, not perfect but a start.
The dropdown next to the open icon in the toolbar is the "Recently opened files list" not the "Recently visited documents" list, so no.