The equality conjecture for the GY and projective extended TQFT bimodules

Let $F$ be a zero-decorated admissible $2$-dimensional cobordism from $M_1$ to $M_2$, where every component of $F$ intersects the incoming boundary $M_1$. Let $A_{EF}(M_i)$ denote the algebra $\left(U(\mathfrak{psl}(1|1))\right)^{\otimes p_i}$ associated to $M_i$, and let $\mathbf{Z}^{GY}_{\operatorname{ext}}(F)$ and $\mathbf{Z}^{P}_{\delta_{1/2},\pi_{1/2}}(F)$ be the resulting $\mathbb{Z}$-graded bimodules over $(A_{EF}(M_2),A_{EF}(M_1))$.

Equality conjecture. If each component of $F$ intersects $M_1$, then, as $\mathbb{Z}$-graded bimodules over $(A_{EF}(M_2),A_{EF}(M_1))$,

$$\mathbf{Z}^{GY}_{\operatorname{ext}}(F)\cong \mathbf{Z}^{P}_{\delta_{1/2},\pi_{1/2}}(F).$$

The admissibility hypothesis ensures that these bimodules are projective as left $A_{EF}(M_2)$-modules. The source gives no evidence that the proposed identification has been proved or disproved.