The reason you mention is teh most common.
Also look into: In the support article: If you subscribe to Apple One and use a different Apple ID for iCloud - Apple Support Apple makes sideways reference to using a different Apple ID for media subscriptions and purchases but doesn't describe how to do this.
In iOS/iPadOS: Go to Settings > [your Apple ID] > Media & Purchases. Sign out of your current ID and sign in with a different one.
If you still have questions or problems:
Refer to this document for ways to contact Apple --> Choose your country or region - Official Apple Support
Select your country (also look for "other" regions), then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.
or:
Contact Apple for support and service by telephone --> Contact Apple for support and service - Apple Support