Split-generation conjecture for the ungraded mirror of the real projective plane

Let $Q_{d53f\mathbb{R}P^2}$ denote the matrix factorization corresponding, under homological mirror symmetry, to the monotone Lagrangian $(\mathbb{R}P^2,b=0)$, and let

$$W=x+y+\frac{1}{xy}.$$

Here ${\sf MF}^{un}(W)$ is the ungraded category of matrix factorizations of $W$. Split-generation conjecture. The object $Q_{\mathbb{R}P^2}$ split-generates the category

$${\sf MF}^{un}\left(W=x+y+\frac{1}{xy}\right).$$

This conjecture is motivated by homological mirror symmetry: the corresponding Lagrangian split-generates the Fukaya category of $\mathbb{C}P^2$, so its mirror matrix factorization is expected to split-generate the ungraded matrix factorization category. The supplied text does not state whether the conjecture has been proved or disproved.