Sign in to your Microsoft Account and under Services & subscriptions, confirm that you see something like this with install buttons so you can just install Office 2021 for Mac on the 2024 Macbook Pro. If true, then do the following paragraph to remove Office 2021 from your old MacBook Pro, and when done, sign in to your Microsoft account on the 2024 MacBook Pro and click the Install button.

I moved an initial Office 2021 for Mac installation from Big Sur running on an M1 MacBook Pro to an M1 Mac mini. I removed all of the Office 2021 bits on my MacBook Pro using Microsoft's recommendations for that process. On the M1 mini (now M2 mini Pro), I signed into my Microsoft account and clicked the Install button for Office Home & Business 2021 for Mac and it did so without my having to enter any product key.
I happen to also have Office 2021 installed under Windows 11 Pro (Parallels guest) on an Intel iMac.
Each of my Office 2021 licenses cost me around USD 34 from Stack Social.