Could you check the Settings/Preferences page, Search panel. This article can get you to that section of the settings: [[Change your default search settings in Firefox]]. Toward the bottom there is a box labeled Shortcuts. Normally you would find both Google and DuckDuckGo listed in this box because they are built-in options. If Google and/or DuckDuckGo is not listed, could you scroll down below the box and click the "Restore Default Search Engines" button and see whether that brings them back.