Formality-independence of the quasi-classical limit of a DQ-algebroid

Let $\mathcal{C}$ be a DQ-algebroid, let $(\pi_t,H)$ represent its equivalence class under the bijection induced by a choice of a formality isomorphism, and let $\Pi$ be the Lie algebroid associated with the Poisson bivector underlying $\pi_t$. The quasi-classical limit $\widetilde{\operatorname{gr}^\times}\mathcal{C}$ and the associated graded algebroid $\operatorname{gr}^\times\mathcal{C}$ equipped with the $\Pi$-connective structure with flat curving deduced from $(\pi_t,H)$ are the objects under consideration.

Formality-independence claim. The quasi-classical limit $\widetilde{\operatorname{gr}^\times}\mathcal{C}$ is equivalent to $\operatorname{gr}^\times\mathcal{C}$ equipped with the $\Pi$-connective structure with flat curving deduced from $(\pi_t,H)$. Moreover, this equivalence is independent of the choice of formality isomorphism.

This identifies the quasi-classical limit with geometric data determined by the quasi-classical Poisson and gerbe data, and asserts that the resulting equivalence does not depend on the auxiliary formality choice. The supplied text does not state whether the claim has been proved or remains open.