We contact our servers only to verify receipts when you buy Pro (had some issues with that earlier :$). We also use analytics for crash reports.

Everything else is either direct to https://news.ycombinator.com or https://hacker-news.firebaseio.com (the official API). And, of course, sites explicitly opened by the user.

Edit: We also use the readability API for reading mode. https://www.readability.com/