Microsoft 365 features that help users manage their subscriptions, account settings, and billing information.
it is happening on my macbook. Login on microsoft online works. Also Office 365 online works. But whenever I go and Open Word, Excel or Powerpoint I get sign up/activate.
Since you have a Microsoft 365 subscription, you should be able to install and activate Office locally on your Mac. You do need Microsoft 365 Personal, Family or Premium (or one of the corresponding business/organization subscriptions). In particular, note that 365 Basic won't let you install and license Office apps locally (Basic subscriptions include OneDrive storage and mobile apps only).
Which version of macOS do you have? You will need macOS 12 or later. Depending on your specific version of macOS, you may not be able to run the most recent Office release, though. See https://www.brandwares.com/bestpractices/2023/03/most-recent-office-you-can-run-best-practices/ .