A family of Microsoft word processing software products for creating web, email, and print documents.
In one-time-purchases of Office, you do not need to be signed in, so Step 1 isn't relevant.
For step 4 in Word for Mac, choose Word>About Microsoft Word. The dialog that opens should show you Microsoft account email address beside Belongs to:. Click on More Info, then on Refresh License, Word will ask you to sign in, after which it will hopefully reconnect your account with your installation.
If that doesn't fix it, try creating a new user account (System Settings>Users & Groups), signing in to that, then testing if the problem still exists. If it goes away, it's an issue with the user profile part of your Office installation.
If the issue still exists, or you'd rather not move your user data to a new profile, then uninstall Office following these steps: Uninstall Office for Mac Then reinstall from the Subscriptions page of your Microsoft account.