The Bridgeland conjecture for Enriques realizable K3 surfaces

Let $S$ be an Enriques realizable K3 surface, meaning a K3 surface arising in the Enriques-related moduli setting considered in the source. Bridgeland conjecture. $S$ is Bridgeland. The source motivates this as a reasonable conjecture after an example, but gives no further formulation or evidence of resolution.