JSON schema is not registered with Schema Registry

With the following Kafka Connect connector configuration:

{
  "name": "Migrations_20250227172534930",
  "connector.class": "SqlServerCdcSourceV2",
  "kafka.auth.mode": "KAFKA_API_KEY",
  "kafka.api.key": "",
  "kafka.api.secret": "",
  "database.hostname": "",
  "database.port": "1433",
  "database.user": "",
  "database.password": "",
  "database.names": "db",
  "snapshot.isolation.mode": "snapshot",
  "table.include.list": "dbo.Migrations_20250227172534930",
  "tasks.max": "1",
  "topic.prefix": "migrations",
  "max.batch.size": "1",
  "value.converter": "io.confluent.connect.json.JsonSchemaConverter",
  "value.converter.auto.register.schemas": "true",
  "value.converter.schema.registry.url": "https://psrc-123456.germanywestcentral.azure.confluent.cloud",
  "value.converter.basic.auth.credentials.source": "USER_INFO",
  "value.converter.basic.auth.user.info": ":"
}

I am hoping to have the JSON schema automatically registered based on the messages published. The messages are published successfully, but no schema is registered.

If I change the converter to io.confluent.connect.avro.AvroConverter, the schema is registered successfully.

What am I missing?