I subscribed to Apple One using my APPLE ID account

See the subscription process in the article below.

Apple One - Get

How to get Apple One

1. On your iPhone, iPad, or iPod touch, go to Settings > [your name] > Subscriptions. Or go to your subscriptions settings. 
2. Tap Apple One. 
3. Choose a plan.
4. If you already subscribe to Apple Music, Apple News+, Apple Arcade, or Apple TV+, you don't need to cancel those subscriptions. They will automatically be canceled when you're billed for Apple One.

Cancel the subscription on the APPLE ID account and then subscribe with the PURCHASE ID.

Purchases - View, change, or cancel your subscriptions.        

Apple One - Get