RC-positive tangent bundle conjecture for rationally connected manifolds

Let $X$ be a projective manifold. A projective manifold is rationally connected when any two points can be connected by a rational curve, and $T_X$ denotes its tangent bundle.

RC-positive tangent bundle conjecture. If $X$ is rationally connected, then $T_X$ is RC-positive.

By the theorem immediately preceding this conjecture, the assertion is a special case of the paper's broader equivalence conjecture for vector bundles. The source does not provide a resolution status for this special case.