How can I get a refund for an unintended subscription charge from Apple?

The policy is that all transactions in the App Store are final. The reason for that is that to start a free trial/subscription it requires that you double click the side button with the trial period on the screen and a message that you will be billed for the subscription if you do not cancel at least 24 hours before the trial period ends. That is what you had agreed to when you started the free trial. It may be helpful to set a reminder to cancel the free trial if that is necessary, and forgetting to cancel is not likely going to result in a refund. At times, Apple may provide a compassionate refund, but it should never be expected.

Cancelling the subscription does prevent it from being renewed, and you still have the service that you have paid for until the expiration date. There is not an option to cancel a subscription that results in a refund of any remaining subscription that is unused.