I do not know that Office 2024 is substantially better than Office 2016. I am using 365 and do not necessarily like the "improvements."


Assuming that you registered your 2016 with your office account, log in on your new computer, go to the Services & Subscriptions tab and scroll to the bottom of the page where Office 2016 should be in your purchases. Click on it to get a link to download.


You may have to deactivate the installation on the old computer. That is also done on that account page.