Are the Sspx chapels under diocesan bishops?
At least partially, yes (ie., the SSPX will not perform weddings without receiving the delegation from the local bishop, and in France, when a couple was married without it by one of their priests, the SSPX applied to a bishop for a sanatio in radice).
Doing that suggests the SSPX believes it’s marriages are invalid without the delegation.
Should the rest of us married by the SSPX without delegation also now be required to apply to the local bishop for sanation of our marriages?