The settings at the URL opera://settings/searchEngines are for the address field and not for the search field on the start page. The search field on the start page is fixed to a specific search engine based on your locale.
If you want something different for the search field on the start page, goto the URL opera://about, take note of the "profile" path, close Opera and edit the "Local State" file. It'll be one level up from the profile folder in you're using Opera One and in the profile in you're using Opera GX.
In the "Local State" file, change the country and country_from_server values to the country code you want like US for example.