Tapping to select a new search engine should not immediately perform a search

[data-sync-user]

Selecting an alternative search engine (besides the default) should no longer automatically perform a search, but instead allow the user to continue modifying their query.

This will require some re-architecting to update SearchSuggestClient’s searchEngine with the newly selected engine.

A selected engine’s override should only remain until a search is performed. Then the default search engine should once again be used.

┆Issue is synchronized with this Jira Task