Omnisearch — the already excellent Obsidian search plugin — has added a new option, to show relevant notes from your Obsidian vault alongside organic web search results.
I don’t know about the password protection: it’s not referenced in the omnisearch documentation.
Re: publishing. To clarify, Omnisearch will surface relevant notes from your vault, regardless of whether they’ve been published or not. However, Omnisearch has an optional setting which can respect your excluded files as defined in Obsidian’s first party settings.