At least on desktop persistent search features are currently limited to search engines pre-configured by the Firefox team. So on desktop, if you add a search engine Fx team won't hide the URL and display the search term while you search with that eng...
Hey SouthFresh,You can go to about:preferences, and navigate to the search settings. Find the setting for "Show search terms in the address bar on results pages" and flip the checkbox to turn off the persistent search term feature.