Purity implies formality for quantised orientation modules

Let $(\mathrm{X},\sigma)$ be a holomorphic symplectic manifold and let $\mathfrak{L}$ be a countable collection of orientable compact Lagrangian submanifolds such that the weight filtration of $\mathrm{H}\mathcal{DQ}_\mathfrak{L}(\mathrm{X},\sigma)$ is pure. Purity-formality conjecture. The differential graded category $\mathcal{DQ}_\mathfrak{L}(\mathrm{X},\sigma)$ is formal. This is an instance of the principle that purity of a mixed Hodge structure should imply formality; the paper does not establish the assertion in this generality.