Effective descent conjecture for finitely presented module spectra

Let $A,A_1,A_2,A_{12}$ be noetherian $\mathbb{E}_1$-Banach rings in the indicated simplicial ind-Banach categories. Suppose that their homotopy rings fit into a short strictly exact gluing sequence

$$0\longrightarrow\pi_0(A)\longrightarrow\pi_0(A_1)\oplus\pi_0(A_2)\longrightarrow\pi_0(A_{12})\longrightarrow 0,$$

that the images of $\pi_0(A_i)$ in $\pi_0(A_{12})$ are dense, that each map $\pi_0(A_i)\to\pi_0(A_{12})$ is flat, and that $A,A_1,A_2,A_{12}$ form the corresponding derived gluing sequence. Effective descent conjecture. The map $A\to\prod_{i=1,2}A_i$ is an effective descent morphism with respect to finitely presented left module spectra, meaning modules whose $\pi_0$ is finitely presented. This asserts descent for finitely presented module spectra in the derived gluing situation; the supplied text gives examples motivating the setup but does not state whether the claim has been proved or disproved.