Thanks for the follow-up.

That's a good catch! {Z2, Z3} is indeed a sufficient set becuase it blocks all back door paths between X and Y.

This is true for the same reason that {Z1, Z2, Z3} and {Z1, Z3} are sufficient sets. Although we "unblock" the back door path (X <- Z1 -> Z3 <- Z2 -> Y) by conditioning on the collider Z3, we can still block the path by conditioning on either (or both) of Z3's parents.

Hope that clears things up!