I accidentally had two accounts in two different email addresses.

On the iMac, Office is still tied to the cancelled Personal subscription, so it must be signed out and reactivated with the account that owns the Microsoft 365 Family subscription.

Follow these steps on the iMac:

1. Sign out of Office and sign back in
   1. Open any Microsoft 365 app (for example, Word).
   2. Select the name/profile icon at the top.
   3. Choose Sign out of all accounts.
   4. Close the app, then reopen it.
   5. Select Sign in and enter the email address that has the active Microsoft 365 Family subscription (this will be the account shown under Services & subscriptions at https://account.microsoft.com/services).
   6. Let Office complete activation.
2. Make sure the correct account has a valid subscription
   1. In a browser, go to https://account.microsoft.com/services.
   2. Confirm that the Family subscription is listed and active for the email address being used to sign in on the iMac.
3. If activation still fails with an account error
   1. On a Mac, if Office is still trying to use the old/cancelled account, remove the old license files as described in How to remove Office license files on a Mac.
   2. After removing the license files, reopen a Microsoft 365 app and sign in again with the Family subscription account.

If the iMac was previously signed in with both a personal Microsoft account and a work/school account, ensure the sign-in used for activation is the personal Microsoft account that owns the Family subscription.

References:

• Microsoft 365 Apps activation error: "That Microsoft account doesn't exist. Enter a different account or get a new one."
• About accounts in Office
• I forgot the account I use with Microsoft 365
• How can I upgrade from a Microsoft 365 Personal to Family subscription?