The product key for Office 2016 is typically associated with a specific number of activations based on your volume licensing agreement. If you purchased a retail version of Office 2016, it generally allows installation on one computer at a time. If you need to install it on a new computer, you would need to deactivate it on the old one first.
This policy has been consistent, and if you are now being informed that you can only use the product key on one computer at a time, it is likely not a change in policy but rather a standard enforcement of the licensing terms.
If you want to install Office on multiple computers, you may need to consider purchasing additional licenses or a different licensing option, such as a subscription to Microsoft 365, which allows for installations on multiple devices depending on the plan.