The logical negation of “identical” is simply “not identical.” If technical “otherness” additionally requires possible separation, it is no longer the bare logical contradictory of identity.
The formula can then mean: the attribute is not conceptually interchangeable with the essence, yet it is not an independently separable being. These statements concern different respects and should not automatically be treated as simultaneous denial of a single exhaustive pair.
This is a clarification of terms, not an exemption from logic. Genuine contradictions remain impossible; the issue is how “identity” and “otherness” function in this specific theological usage.