monkey34 Brave has a new search engine at https://search.brave.com/. While it's still in beta, I've found it to be mostly good, and it might be worthwhile to add it to the list of default search engines in the preferences dropdown.
h2flux If Brave Search gets added, I'd also suggest adding other search engines like StartPage and Qwant. I found a comprehensive search & suggestion URL list: https://forum.vivaldi.net/topic/16991/guide-search-suggestion-url/15?lang=en-US# (The table is somewhere on the linked forum thread. The link takes you slightly under the post, so scroll up.)
czj You can add a custom search engine via the "manage" option. Adding Ecosia, Brave Search, Qwant and many other good alternatives might make the list very long.
cnrca Seems that there are more work to support different types of response in suggestions: https://search.brave.com/api/suggest?q=%s&rich=true&source=web does not seem to be working.