Transfer Microsoft apps to a new Mac

Do you mean that you bought a one-time purchase version of Microsoft Office a year ago? Or that you took out a one-year subscription to Microsoft 365?

Microsoft Support – Transfer your Office license to another device or another person

You may want to check with Microsoft as to whether the version of Office that you want to transfer would work on the new Mac.

Microsoft – Microsoft 365 and Office Resources

Microsoft Support – Office 2019 for Windows and Mac FAQ

I didn't. I installed my Office 2016 suite on the original Mac, then with Microsoft's help, got it activated on a different Mac.

MS no longer does phone activation, you have to chat with the tech rep. But that was, amazingly, a painless experience.