I built a desktop browser extension version (100% open source and GPL licensed) of this basic idea or side searching filtered to some sites only. It also just uses your browser's default search engine (so you can stick to DuckDuckGo for example). Usually I don't like to plug on HN but thought this is uniquely relevant.
It shows reddit (also HN, and others when relevant) filtered results in a sidebar for Google queries. It's auto expanded when there's a non-navigational query with no onebox (this is a increasingly becoming a good indicator of when Google is lacking decisiveness in a query).