Show site URL in Omnibox after running a search

Problem: you open Brave and type in “brave nightly” in the omnibox and press enter to search.
You now want to copy the URL of the page of results to another browser, however, the omnibox still just has your query in it, there is no URL.
Note that the google page shown also includes the query information, so it is redundant.

Request: Upon executing a search from the omnibox, show the URL of the resulting page.

Note that this isn’t the only issue with the omnibox, it also shows the text: chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/
before any PDFs, which breaks web clipping apps as well as cut-n-paste sharing of the PDF.
The chrome-extension information should be trimmed from the omnibox display.