Since they implemented privacy pass, there is now something stopping them from doing both. See https://help.kagi.com/kagi/privacy/privacy-pass.html

Obviously with it you trade the need to trust them for your own personalization (as they can’t know it was you searching).

The other user already shared some article with lots of historical data, both words and actions, that should give a better picture. Anyway, since you decided to ignore all that, then there is also to say that the tweet was a speculation made months ago on a topic where nothing happened yet (or at least, I haven’t read any news about antitrust in the last month). I don’t think anything will happen, but anyway that makes it at most naive.