A family of Microsoft word processing software products for creating web, email, and print documents.
Sorry to hear about this. Could you please confirm whether this happens with every Word document or only with older existing files? Also, are you able to create a new blank Word document and save it successfully to a local folder such as Documents or Downloads, rather than the Desktop?
Please also confirm which version of Word for Mac you are using by going to Word > About Microsoft Word, and whether Word shows any activation or sign-in warning under your Microsoft 365 account. If you receive any error when using File > Save As, please share the exact message or a screenshot with any personal information hidden.