Harris–Tschinkel potential-density conjecture for varieties with negative canonical bundle

Let $V$ be a variety over a number field. Its rational points are potentially dense if there is a finite extension $K'$ of the ground field such that $V(K')$ is Zariski dense in $V$.

Harris–Tschinkel conjecture. Rational points are potentially dense on

1. all Fano varieties;
2. in the stronger form, all varieties $V$ such that $-K_V$ is nef.

The conjecture proposes potential density for varieties with negative canonical bundle. The source presents it as a proposal of J. Harris and Y. Tschinkel and gives no resolution status.