I am interested in developing an add-on which displays the installed search engines and lets you select the one to be the default search from the tool bar.
Is this functionality available the in the current API?
A search engine can set “is_default” when declared in an extension: https://developer.mozilla.org/en-US/Add-ons/WebExtensions/manifest.json/chrome_settings_overrides
Extensions can currently not list and modify the default search engine, though I think APIs are in the work to at least let you list search engines.