Let $\mathfrak{g}$ be a semisimple Lie algebra, $\mathfrak{g}^L$ be its Langlands dual. Feigin--Frenkel duality says $$ W^k(\mathfrak{g})=W^{k_L}(\mathfrak{g}^L) $$ if $r'(k+h^{'})(k_L+h'_L)=1$, where $r'$ is the maximum number of edges between two vertices in the Dynkin diagram of $\mathfrak{g}$, $h'$ (resp. $h'_L$) is the dual Coxeter number of $\mathfrak{g}$ (resp. $\mathfrak{g}_L$).

A degeneration of this result when $k_L$ tends to infinity was used as local input by Beilinson--Drinfeld to establish some results on geometric Langlands (which was globalized using the theory of chiral algebras). Regarding the non-degenerate result, they say "We do not know if this “doubly quantized” picture can be globalized." Has the non-degenerate result been globalized in some way since then?