Have stats from online play figured into the design process?
I don't even see how this could happen. Like, I guess I could find out that an effect was stronger than I expected; except, I would already have found that out other ways.
Lots of ways, and that's without "rate your game" or "veto mode" features to evaluate enjoyment and popularity respectively.
For example, you could see how many cards Farming Village reveals on average, and whether that draw effect is worth pursuing on another card (eg a card that draws until it reveals an action or treasure, then discard for benefit). See how well an effect actually works, beyond just how strong a card is.
Deconstruct how a card works as a springboard for ideas. An analysis of how remodel is used (ie often less than 2 more) would have easily led to the idea for Butcher (what if you got rewarded for not using the full remodel).
Or you could see how often effects like Vagrant, Merchant etc. actually work to set benchmarks for new conditional cantrips.
Big data is useful in general. Which cards are associated with ragequits? What cards are popular with beginners/intermediate/experts (so you can design a mix to have the right appeal)
And then there's revising expansions (or designing new cards that better achieve the concepts of old cards).