Another option is SearXNG. It's meta search engine, which means that it aggregates other search engines like Google and Bing but without tracking or logging, because your searches are proxied using a public instance, that will mix your search with the ones from other people.
And about default search engine, don't know what you're talking about, both chrome and Firefox allows this, in mobile and desktop.
I host it in a Truenas BSD Jail, and the process was as straightforward as compiling and running any other Rust / Postgres project. Which error did you get?