Isn't brave supposed to be "private"?

No. At least not in the way most people expect.

It does block some tracking and ads that Chrome alone allows or explicitly adds. But it simply shifts that tracking to Brave. The idea was that you'd still get the benefits of that tracking by giving all of your data to Brave instead. I honestly never was convinced by this considering your data is still being sold, just by a different company so it doesn't sound much better to me. Supposedly, according to them, Brave is more trustworthy and gives you more control over what they track and sell, but I don't trust that business model. There's no real incentive for them to do what they said they would.