Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Hi
You do not need to manually “add” the new computer to Microsoft 365 Personal. The PC becomes activated when you install Office and sign in with the Microsoft account that owns the subscription. Microsoft confirms this here: https://support.microsoft.com/en-us/accounts-billing/subscriptions/sign-in-to-microsoft-365
First confirm your paid Microsoft 365 Personal appears as Active here: https://account.microsoft.com/services
Then open Word on the new PC > File > Account > Sign in, and use that same account.
Important: if Windows then asks you to create/enter a PIN or says “Use this account everywhere on your device,” look for “Microsoft apps only” / “This app only” instead of continuing with the PIN setup. This signs the account into Office without changing the way you sign in to Windows. Microsoft documents this option here: https://support.microsoft.com/en-us/accessibility/teams/use-a-screen-reader-to-set-up-teams-for-personal-and-small-business-use
There is no need to keep uninstalling and reinstalling Office.
If “Microsoft apps only” is not shown, please tell us the exact wording on the PIN screen (or post a screenshot with your email hidden). That will identify which Windows sign-in prompt is blocking activation.