Safari no longer available as my preferred browser

Yes, those are your only choices for search engines. They have nothing to do with what your default browser is.

See here for additional information.

Change the default web browser or email app on your iPhone, iPad, or iPod touch - Apple Support

What other browsers do you have installed on your Mac? What version of macOS are you using? What model Mac?

Okay, you've posted in the Mac forum.

What you're looking at is Settings>Safari>Search Engine. That allows you to choose your default search engine, not browser. There is no "Safari" search engine.

Safari is the default browser unless you've explicitly made something else the default browser.