Splitting conjecture for Floer spectra of del Pezzo complements

Let $M$ be a del Pezzo surface of degree $1$, $5$, or $7$, and let $D$ be a generic smooth representative of $M$'s anticanonical divisor. A stable $\mathbb{R}$-polarization of $X$ is a stable $\mathbb{R}$-polarization $\Lambda$ of $X$; let $V_1,\ldots,V_k,\ldots\to M$ be real vector bundles, with $V_0$ appearing in the asserted decomposition. Splitting conjecture. There exists a stable $\mathbb{R}$-polarization $\Lambda$ of $X$ and real vector bundles $V_1,\ldots,V_k,\ldots\to M$ such that

$$\mathfrak{F}^\Lambda\simeq\mathfrak{D} X^{-V_0}\vee\bigvee_{k\geq 1}\mathfrak{D}(S_D M)^{-V_k}.$$

This conjecture predicts a stable splitting of the Floer spectrum associated with the complement data for del Pezzo surfaces of the specified degrees. The surrounding discussion presents it as a consequence suggested by the paper's computations; no resolution is supplied here.