How do I load a JWK into a Java PublicKey object?

Question

I currently have a JWK public key in the following json format(in a file called public_key.json, that public key is a sample):

{
    "productId": "some-product",
    "kid": "abc123...",
    "exp": 1669574140,
    "y": "ABC....",
    "kty": "EC",
    "use": "enc",
    "alg": "ECDH-ES",
    "crv": "P-521",
    "x": "DEF..."
}

I am loading the JWK with the following code:

import java.io.IOException;
import java.nio.file.Files;
import java.nio.file.Paths;
import java.security.KeyFactory;
import java.security.NoSuchAlgorithmException;
import java.security.PublicKey;
import java.security.spec.InvalidKeySpecException;
import java.security.spec.X509EncodedKeySpec;

class Sample {
    public static void main(String[] args) {
        try {
            byte[] payload = Files.readAllBytes(Paths.get("public_key.json"));
            KeyFactory otherkf = KeyFactory.getInstance("EC");
            X509EncodedKeySpec pkSpec = new X509EncodedKeySpec(payload);
            PublicKey publicKey = otherkf.generatePublic(pkSpec);
            
        } catch (IOException|InvalidKeySpecException|NoSuchAlgorithmException e) {
            e.printStackTrace();
            System.out.println(e);
        }
    }
}

The above code is raising the following exception:

java.security.spec.InvalidKeySpecException: java.security.InvalidKeyException: invalid key format
    at jdk.crypto.ec/sun.security.ec.ECKeyFactory.engineGeneratePublic(ECKeyFactory.java:158)
    at java.base/java.security.KeyFactory.generatePublic(KeyFactory.java:351)
    at Sample.main(Sample.java:16)
Caused by: java.security.InvalidKeyException: invalid key format
    at java.base/sun.security.x509.X509Key.decode(X509Key.java:387)
    at java.base/sun.security.x509.X509Key.decode(X509Key.java:402)
    at jdk.crypto.ec/sun.security.ec.ECPublicKeyImpl.<init>(ECPublicKeyImpl.java:71)
    at jdk.crypto.ec/sun.security.ec.ECKeyFactory.implGeneratePublic(ECKeyFactory.java:225)
    at jdk.crypto.ec/sun.security.ec.ECKeyFactory.engineGeneratePublic(ECKeyFactory.java:154)
    ... 2 more

Am I loading the public key properly or do I need to transform the json into another format?