the Windows Search Provider App Extension lets you replace bing with your own search engine. the MISX package just registers an extension that will be used by the builtin server provider. It does not replace the search provider, the extension just specifies the url to call for search.
so the "com.microsoft.windows.websearchprovider" just specifies the component the extension will be used by. you can not change this.
your WISX component just registers the url of your custom server provider, and a couple formatting options. your custom url endpoint will respond to get request with a json response. as there is no UI, so there is no authentication. not sure if cookies are supported, but they would be treated as 3rd party cookies so might be stripped.
note: this feature is only available in the EU.