Converting Secure Enclave protected SecKey to SecureEnclave.P256.Signing.PrivateKey

Is it possible?

The original key was generated and stored in the Keychain using the following code:

func generateSecureEnclaveProtectedSecKey(withTag tag: Data) throws -> SecKey {
    var error: Unmanaged<CFError>?
    let accessControl = SecAccessControlCreateWithFlags(
        kCFAllocatorDefault,
        kSecAttrAccessibleWhenUnlockedThisDeviceOnly,
        [.privateKeyUsage],
        &error
    )!

    let attributes = [
        kSecAttrKeyType as String: kSecAttrKeyTypeECSECPrimeRandom,
        kSecAttrKeySizeInBits as String: 256,
        kSecAttrTokenID as String: kSecAttrTokenIDSecureEnclave,
        kSecPrivateKeyAttrs as String: [
            kSecAttrCanSign as String: true,
            kSecAttrIsPermanent as String: true,
            kSecAttrApplicationTag as String: tag,
            kSecAttrAccessControl as String: accessControl,
        ] as [String: Any],
    ] as [String: Any]

    let privateKey = SecKeyCreateRandomKey(attributes as CFDictionary, &error)!

    return privateKey
}

Then I wanted to use the strongly typed interface of CryptoKit, so I naively tried to get a hold of the existing key as follows (querying for kSecReturnPersistentRef and not kSecReturnRef):

func getSecureEnclaveProtectedCryptoKitKey(fromSecureEnclaveProtectedSecKeyWithTag tag: Data) throws -> SecureEnclave.P256.Signing.PrivateKey {
    let query: [String: Any] = [
        kSecClass as String: kSecClassKey,
        kSecAttrApplicationTag as String: tag,
        kSecAttrKeyType as String: kSecAttrKeyTypeECSECPrimeRandom,
        kSecReturnPersistentRef as String: true,
    ]

    var item: CFTypeRef?
    let status = SecItemCopyMatching(query as CFDictionary, &item)

    let keyData = item as! CFData

    return try SecureEnclave.P256.Signing.PrivateKey(dataRepresentation: keyData as Data)
}

But that resulted in:

Error Domain=CryptoTokenKit Code=-3 "corrupted objectID detected" UserInfo={NSLocalizedDescription=corrupted objectID detected}

Since this is a Secure Enclave protected key, it is not possible to use SecKeyCopyExternalRepresentation (or query for kSecReturnData), but perhaps there is another way to convert a SecKey object to a SecureEnclave.P256.Signing.PrivateKey?

The other way around seem to be possible using the answers to this blog post: https://developer.apple.com/forums/thread/728314