Good day @Charlie Hale, and I appreciate the clear explanation of your concern.
Office 365 apps for Mac now requires macOS 14 (Sonoma) or later. This is part of Microsoft’s policy to keep apps secure, stable, and compatible with new features. Your wife’s Mac with macOS Ventura 13.7.8 can still use Microsoft 365, but only up to version 16.101, which is the last supported version for Ventura.
Below are the available options that should help you move forward:
Option 1: Install the last compatible version for macOS Ventura (Version 16.101)
This allows continued use of the desktop apps on the current system.
Go to the Microsoft Update history for Office for Mac article.
Locate Version 16.101, which is the last version supporting macOS Ventura.
Download the Install package (ensure it is not labeled as an Update package).

Open the downloaded .pkg file and follow the installation instructions.
Once installed, open an Office app such as Word or Excel.
Sign in using the work account that has the Microsoft 365 subscription to activate the apps.
Important note: The apps will continue to function normally, but no further updates, including security updates, will be provided while staying on macOS Ventura.
Option 2: Use Office 365 apps for the web
This is a good alternative if you prefer not to install an older desktop version.
Open a web browser (Edge/Safari/Google Chrome), then go to the browser settings and clear browsing data. Set the time range to "All time" to avoid issues caused by outdated cache.
Go to https://www.office.com and sign in the work account.
Once signed in, select Apps > Select the app you want to use such as Word, Excel, PowerPoint, or OneNote.

Note: Web apps provide strong functionality, although some advanced desktop features may be limited.
Additional information is available in the following resource: Upgrade macOS to continue receiving Microsoft 365 and Office for Mac updates - Microsoft Support
I’m really sorry, I know this isn’t the outcome you were hoping for. I completely understand how these system requirements can feel limiting, especially when you are simply trying to get things working smoothly on an existing device.
As a forum moderator, I truly want to help point you in the right direction and share the most suitable options available. However, I do not have the ability to change or escalate product limitations.
I hope this information is helpful. If you have any questions or need further support, please don’t hesitate to reach out at any time.
Thank you for your patience and understanding.
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