Langlands' functoriality conjecture for Galois representations

Let $E/F$ be a finite extension, let $\rho:\operatorname{Gal}(E/F)\rightarrow GL_n(\mathbb{C})$ be a representation, and let $L(\rho,s)$ denote its Artin $L$-function. Langlands' functoriality conjecture. There is an automorphic representation $\pi$ corresponding to $\rho$ such that

$$L(\rho,s)=L(\pi,s).$$

This is presented as an instance of Langlands functoriality and as a non-abelian extension of Artin reciprocity; the source says it implies Artin's holomorphy conjecture using the known pole behavior of automorphic $L$-functions, but gives no resolution status for the assertion itself.