How can I change the search engine from Yahoo in the "Firefox Search" search provider?
If you tap on one of the search engine, it should give you this dialog box which you can tap on "Set as default":



I tested it on a Nexus 6 and it does switch the search provider used in the Home-button swipe search.

If this dialog doesn't appear for you or if the "Set as default" here doesn't change your search in both the URL bar and Home Button search, then it would be a bug. You might want to report the bug in Bugzilla@Mozilla, with your device and OS version.