I was going to suggest that search should just redirect to DDG or Brave search with the !hn tag, but I tried it out and both of those just redirect to the same

I was going to suggest that search should just redirect to DDG or Brave search with the !hn tag, but I tried it out and both of those just redirect to the same search page that HN uses (hn.algolia.com). That's both really nice because why not have your site-specific search results reference the search page that site uses and really annoying if the problem is that that page's search doesn't work very well. It looks like redirecting the search to "site:news.ycombinator.com" does leverage their individual search results instead of going to algolia.com, so that's still an option.