What was going on
Upgrading Crossplane hit a crash loop in the core pod with crossplane: error: cannot initialize core: cannot apply crd: cannot patch object ... status.storedVersions: Invalid value: must appear in spec.versions. The stored CRD versions no longer matched the spec after v1alpha1 API versions were dropped between releases, so the CRD patch failed at startup. One reporter hit it going from 1.12 to 1.13.
What fixed it
Fixed in the v1.13.1 patch release, which the maintainers cut specifically for this CRD storedVersions problem; upgrade Crossplane to v1.13.1 or later. A reporter confirmed 1.13.1 resolved the same failure on the 1.12 to 1.13 path. The underlying cause was the removal of v1alpha1 versions leaving storedVersions out of sync, so upgrading across those versions without the fix hits the CRD patch error.