Eek!
Was my first response on reading it, but tbh on reflection, there isn't really anything in my ChatGPT conversations that I would mind a human reading, and I expect the same for Bard (as long as it's disconnected from my login, which this policy mentions they do). It just feels weird that your "conversation" could be intruded upon and inspected by third parties at any point in the future.
(They also mention that you can "pause saving Bard activity", but knowing Google, that probably results in you not being able to access any Bard history whatsoever, even if saved in the past.)