Serre-geometric locus conjecture for proper Fourier–Mukai partners

Let $\mathcal T$ be a triangulated category with $\operatorname{FM} \mathcal T\operatorname{NE}\emptyset$. The proper Fourier–Mukai locus is $\operatorname{Spec}^{\mathsf{pFM}}\mathcal T$, and the Serre-geometric locus is $\operatorname{Spec}^{\mathsf{SG}}\mathcal T$. Serre-geometric locus conjecture.

$$\operatorname{Spec}^{\mathsf{pFM}}\mathcal T=\operatorname{Spec}^{\mathsf{SG}}\mathcal T.$$

The source presents this as a weaker and more dg-categorical version of the preceding locus conjecture, with no resolution given.