I will compare and contrast a few different constructions of a perverse sheaf associated to a holomorphic lagrangian intersection in a complex symplectic manifold. In particular, work of Brav-Bussi-Dupont-Joyce-Szendroi provides one such construction (the DT-sheaf) via stabilization of vanishing cycles. On the other hand, deformation quantization a la Kashiwara and Schapira provides another construction that is a priori of a somewhat different nature. In joint work with Pavel Safronov, we show that these perverse sheaves are isomorphic in a suitable sense. This provides access to additional structure that was not readily visible on each side. Notably, our isomorphism provides a construction of a DT-sheaf-theoretic holomorphic Fukaya-category, as conjectured by Joyce. As a motivating example, the representation variety of a 3-manifold can be realized as such a lagrangian intersection, leading to insights on the state space of the 3-manifold in the geometric Langlands topological field theory.