I want to request a refund for a subscription. But It doesn't work(

You can contact Apple directly here:

Contact Apple Support - Apple Support

Confirm you have canceled any subscription automatic renewal (if you simply delete an app this does not cancel subscriptions):

Review the information in this support article by clicking on the link to learn how to cancel a subscription from Apple. ➔ If you want to cancel a subscription from Apple - Apple Support

If you subscribed to this directly with a third party, see: About purchases not billed through the App Store or Apple In-App Purchase - Apple Support instead. You need to work directly with the vendor, not Apple.

• Read the article to see what to do about subscriptions that do not appear in your list. If you still can't find a subscription, contact Apple Support using the link at the end of the support article.

• Canceling a subscription does not automatically start a refund.

If you wish to pursue a refund, follow the directions in this support article about how to request a refund for apps or content that you bought from Apple ➔ Request a refund for apps or content that you bought from Apple - Apple Support According to Apple’s terms, refunds are only made to remedy defective or unavailable product. You can request a refund on other grounds but those refunds are entirely discretionary and not guaranteed. Special terms also apply for some countries: About canceling subscriptions in Germany, Israel, South Africa, or Türkiye - Apple Support

Does Apple really no longer have an option for cases where a person forgets to cancel a subscription and wants to cancel the purchase immediately after an annual charge? I made this purchase directly through Apple.

Apple never had a cancel a purchase option that was a user option. (I don't know if they could do this for you if you contacted them and since I have never needed this I don't know.) The procedure has always been if you forgot to cancel a subscription then you paid for it and then asked for a refund. The refund procedure has been unchanged for a a very long time now (I can't remember anything different in the past 20 years).

Unless you subscribe directly with a third party, any subscription will appear on your purchases page. I also provided several links about what to do if you cannot find a subscription, including how to contact Apple. Apple's support is regional and is for people who reside in that area. If they only speak Dutch then that is to be expected and you will have to find a Dutch speaking friend who can help you. If your account is set to a different country then you will have to return to that country to speak with them by telephone. Or if you are lucky you may find a chat option.