Microsoft 365 features that help users manage their subscriptions, account settings, and billing information.
There is no upgrade option as such, the process to switch to another Microsoft 365 subscription is provided on the link below.
To move from the Personal subscription to the Family subscription, basically you purchase a new subscription to the Family version, then the remaining time on the Personal subscription is converted to the Family subscription on a pro-rata percentage basis.
The only other option would be to cancel your existing subscription to get a pro-rata refund, the take out a new Family subscription.
Either way, provided you use the exact same Microsoft account for the new subscription, you will still have access to all your files and the same 1TB of OneDrive storage.