> Biggest advice I can give is you probably don't need search if you're indexable by search bots.

I don't know how relevant it would be today, but ~2005 or so I had a site that used Google search for the internal "search" functionality. It was a webmaster feature of Google at the time, the google results would be displayed with my site's branding, colours, etc. Only results from my site were displayed, but there was a clear Google logo and link at the top. I think that ads were not shown, but I'm not 100% sure.

A/B testing showed significant (I don't remember the numbers) loss of visitors on that page. When presented with our own internal search, visitors would stay on the site the vast majority of the time. But when presented with the google search, visitors would often leave. I would say that the results that google returned were no less relevant than those our internal search provided, in most cases near identical except for ordering.