Not yet reviewed by Pith; the record is open.

Monolayer (ML) transition metal dichalcogenides (TMDs) integrated in optical microcavities host exciton-polaritons as a hallmark of the strong light-matter coupling regime. Analogous concepts for hybrid light-matter systems employing spatially indirect excitons with a permanent electric dipole moment in heterobilayer (HBL) crystals promise realizations of exciton-polariton gases and condensates with immanent dipolar interactions. Here, we identify optical signatures of spatially indirect momentum-bright and momentum-dark interlayer excitons in vertical MoSe$_2$-WSe$_2$ heterostructures and implement cavity-control of both exciton manifolds. Our experiments quantify the strength of light-matter coupling for both zero and finite momentum excitons residing in Moir\'{e} superlattices of TMD HBLs and demonstrate that both exciton species are susceptible to Purcell enhancement in cavity-modified photonic environments. Our results form the basis for further developments of dipolar exciton-polariton gases and condensates in hybrid cavity -- van der Waals heterostructure systems.