Access privileges denied, Word, Ventura 13.3.1

No one else is experiencing this problem. Word is attempting to write the file to a location where it does not have permission to do so. Where specifically are you trying to save the Word documents?

macOS requires the user to grant permissions to save to Desktop, Documents, Downloads, etc. Normally you will be prompted to allow this when you attempt to save to those locations. If you have OneDrive it's possibly your Desktop and Documents have been moved to OneDrive. There is a permission to allow access to OneDrive as well.

Go to System Settings -> Privacy & Security -> Files and Folders and locate Word and click on the > to the left of Word in the listing. It will expand an outline. You may need to turn on Desktop, Documents, Downloads, OneDrive if they are listed. Word will need to be restarted. Then go back and test by saving again in Word.

How to Unlink OneDrive

https://support.microsoft.com/en-us/office/unlink-and-re-link-onedrive-3c4680bf-cc36-4204-9ca5-e7b24cdd23ea

You might not be able to unlink if you cannot login to OneDrive so you will need to reset OneDrive

https://support.microsoft.com/en-us/office/reset-onedrive-34701e00-bf7b-42db-b960-84905399050c

Then you should be able to login to a different OneDrive account.

If your Desktop and Document folders were backed up (moved) to OneDrive we can address that if you have that problem. It was a recent feature that Microsoft added so you might not have this issue.

You might also need to switch accounts if you are using Microsoft 365. I can provide links to remove all Office licensing so you can sign-on with a different account.

Well if you are out of storage space on your cloud then you'll need to take care of that by either freeing up space or increasing your storage.

Are you using Microsoft OneDrive or some other cloud service?

Where are you trying to save it? It sounds like there is some problem with that location. It could be a permissions problem, or something else.