Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Emily has explained the Subscription possibility but if you're using either of the one-time purchase packages (Office 2024, 2021, 2019, or 2016) it's a different story which depends on the specific version. One thing they all have in common is that all can be installed on only one Mac.
Also, if transfer over means by way of Apple's Migration Assistant it may explain the problem. The Migration Assistant primarily is designed for handling user files & Apple's own software. It typically works well for individual applications but often fails with complex integrated suites, especially if the migration involves different editions of macOS on the source & target Macs. In that case it requires removal of the software & performing a fresh installation.