Hi ChromiumIV,
Welcome to community and thank you for sharing the screenshots to describe the issue.
I go through your post carefully and I understand the issue is that the changes you made in Word desktop app cannot sync to SharePoint Server. By saying "SharePoint Server", may I know if you mean SharePoint online in Office 365?
According to the screenshots provided, it seems like you have Windows 7 computer. If yes, the issue may be related to the TLS 1.0&1.1 deprecation by Microsoft and it may affect the connection to Office 365 services.
For the affected computers which have the issue, are they using TLS 1.0/1.1?
If yes, I suggest you try to update to enable TLS 1.2 as default secure protocols in WinHTTP in Windows.
You may try the Easy fix tool from this article and check the outcome.
Update to enable TLS 1.1 and TLS 1.2 as default secure protocols in WinHTTP in Windows
If it doesn't enable TLS 1.2 for you, you may also go to change the registry value:
If issue still happens, for further troubleshooting, could you please confirm information below?
1.For users who have the issue, are they using Windows 7 or Windows 10?
2.Does the issue happen when you edit documents from a specific library? What about if you try a different library or different SharePoint site?
3.What is your Word desktop version? Please go to File>Account, on the right side, capture a full screenshot of Product Information.
Thanks for your patience and effort. Have a nice day and stay safe!
Best Regards,
Tina