Lang's rational-point conjecture for separably rationally connected varieties over $C_1$ fields

Let $k$ be a $C_{1}$ field, meaning that every hypersurface of degree at most $n$ in $\mathbb{P}^{n}_{k}$ has a $k$-rational point. A variety is separably rationally connected if two general points can be joined by a rational curve through which the corresponding evaluation map is separable. Lang's conjecture. Every smooth proper separably rationally connected variety over $k$ has a $k$-rational point.

This conjecture predicts rational points for a broad class of varieties over fields satisfying the $C_{1}$ condition. The source does not state a resolution status for the conjecture.