No, the driver should not return NOT_SUPPORTED, because an application has no good way to react to that. The application would have an operation object that can neither be used nor freed. In practice applications may either ignore errors from abort() or panic.
For multi-part operation, as you mentioned, the abort needs to deallocate resources. If there are some restrictions that prevents deallocating resources in the middle of aead operation, could it be that aead_abort returns PSA_ERROR_NOT_SUPPORTED?