alt Hacker NewsAnthropic explicitly state that they don't do this, even if you use the free plan and even if you don't opt-out of letting them use your data for training:
"We do not sell users’ data to third parties."
https://www.anthropic.com/news/updates-to-our-consumer-terms
That answers for the "sold" part but not for the "used" part.
I.e. nothing about this statement prevents Anthropic from running ads within Claude, as long as they run the ad-placement auctions themselves, and so aren't leaking any of the data they're using to decide which placements are relevant to which users+sessions. (This is the same thing Google does for SERP ad auctions.)
But actually, and perhaps more interestingly, nothing about this statement prevents Anthropic from building a Google AdSense competitor either. Other sites (or mobile apps, etc) could plop in an Anthropic ad iframe; and it'd be Anthropic's knowledge of your interactions with Claude that would drive what ads would show up in that iframe. The embedding site doesn't know what ads the users are seeing, so that's still not "selling users' data to third parties", per se.