I've been struggling for days to resolve an issue with the sudden appearance of a "Update License" message on both my 2023 MacBook Pro, and my 2019 iMac Pro. I made purchases of the Office Home and Business 2021 software for Mac in July 2023 (for the MacBook) and August 2023 (for the iMac) respectively for the above Macs. These are standalone product installations, not the subscription-based 365 products.
I never had any issues with the Home and Business 2021 software until a couple of weeks ago, when following an auto update to the software, I unexpectedly began to see a message instructing me to "Update License" in the Word, Excel and PowerPoint applications. Here's a sequence of screen shots illustrating what occurs, on each of my Macs. The screenshots that follow are from my 2023 MacBook Pro with the following Operating System:

1.) Under "About Microsoft Word, the text "Update License" now appears:

2.) Clicking on "Update License" opens the following pop-up window:

3.) Clicking on the "Sign in" button opens the "Activate Office" pop-up window:

4.) Entering my Microsoft Account email address and clicking on the "Next" button opens an Account Selection pop-up window. I don't have a Work or school account, so I selected "Personal account:":

5.) Following clicking on the "Personal account" selection in the above pop-up window, the following pop-up message is displayed:

In an effort to resolve the error code: 44 problem, I spent at least 10-12 hours trying suggestions that I found on similar threads I found here on the "answers.microsoft.com" website. This included using the Microsoft Office License Removal Tool (multiple times), reinstalling the Office Home and Business 2021 for Mac (multiple times), and nothing has solved the Error code: 44 problem.
You can see a highly detailed post of my extensive efforts on another thread on this website (https://answers.microsoft.com/en-us/msoffice/forum/all/my-word-is-displaying-error-code-44-and-wont-let/b14324e5-037f-410e-a318-71cca0161eb6. See my comments on Pages 1, 2 and 3 of that post. As illustrated on that thread, I've absolutely tried every conceivable action to fix this license-related problem. As stated in the January 30th 2024 Update (documented on Page 3), I have concerns that the recent Microsoft Office software update may have introduced the license issue, as it appears that the "Sign in" screen is referencing a "subscription" and "Microsoft 365" rather than a stand-alone, non-subscription Microsoft Office Home and Business 2021 product.
As I mention on that other thread, The fact that the installations on both the MacBook and the iMac are having the exact same problem, following the installation of Office version 16.81 (24011420), via an auto-update, which occurred on the same day. Note that this version was released by Microsoft on January 16, 2024.
For reference:
Here is the link for the Office for Mac 2021 Update History: https://learn.microsoft.com/en-us/officeupdates/update-history-office-for-mac
Here is the link for the Office for Mac 2021 Release Notes:
https://learn.microsoft.com/en-us/officeupdates/release-notes-office-for-mac
Here is the link for the Office for Mac 2021 <Microsoft AutoUpdate (MAU):
https://learn.microsoft.com/en-us/officeupdates/release-history-microsoft-autoupdate
On the link for the AutoUpdate MAU above, there's a statement regarding the January 2024 release saying: "Changes to support Office 2019 Perpetual License End of Life." There were also "Bug fixes on updates offered". I do wonder if these changes may have contributed to the licensing issues related to the Error Code 44. Please note that I'm also aware of other Mac users that are experiencing the exact same issue as I am.
While I had hoped that other thread would have generated replies from the Microsoft Community's Expert advisory, there's been little in the way of effective solutions offered to date. I'm hoping this new stand-alone post will generate some meaningful help from the Microsoft Product Team of product experts, and I'm looking forward to the replies. Thank You!
Don in Ohio