Microsoft 365 features that help users manage their subscriptions, account settings, and billing information.
You do not need to product code, that is only used initially when you activate your Microsoft 365 Family subscription, after that the Office licence is linked to your Microsoft account as a digital licence.
The full process to share a Microsoft 365 subscription with family members is provided on this link, you basically share your licence with a family member, then send them a share link, they can then use that link to install Office on their devices using their own Microsoft account, then each family members data is kept separate and each member will have their own 1TB of OneDrive storage.