Your purchase was not made with an in-app purchase that is managed by Apple and you are being billed directly through Headway with the credit card information you provided them. That is why it is not showing up as an Apple Account purchase. Unfortunately Apple has to allow a developer to manage their own subscriptions and Headway does offer a Website subscription that includes a Free Trial, where they will bill you directly.
Previously Apple prevented Developers from doing that and was sued and lost, which required them to pay huge fines. Apple followed up by attempting to warn users that their purchase was not being managed by Apple and they were sued again and lost claiming that was an anti-competitive practice and were forced to remove the message. Apple would like to prevent that from happening, but are not allowed to stop it or remove an app that chooses to manage their own subscriptions. Those rules also apply to the Google Play Store.
So now, the leaves you with disputing the charge with Capitol One, and they will also have to block future transactions. If they don't take that extra step to block future transactions and just issue you a new card, you are likely to find that the subscription is moved to the new card, because Capitol One uses an Automatic Billing Updater to prevent disruptions in subscriptions.
The details about the Headway website subscription is seen here in their Privacy Policy, so don't let them tell you that Apple is the only one that manages their subscriptions.
- If you purchased a subscription or enabled free trial on our website: You can cancel a free trial or a subscription by contacting our support at support@get-headway.com or by clicking on “Cancel Subscription” button in your account on our website at least 24 hours before the end of the free trial or then-current subscription period