I use Word 2010, and when I click Save or Save As..., nothing happens. The dialog doesn't even pop up. It's strange because I can create a copy of an existing document and save it just fine.
It turns out that the problem is related to High Contrast Mode. Who would have possibly thought? I use High Contrast Mode #2 in Windows, and when I tried to save the document, nothing happened. When I switched back to regular mode (Left Alt + Shift + Prt Scr), the save as dialog popped up just fine as if nothing was a problem.
I got some help from an answer over here: https://answers.microsoft.com/en-us/office/forum/office_2010-office_install/save-as-dialog-box-does-not-appear-cannot-save/62f0940b-5ba3-4b52-89c6-569d29a4debb?page=2
As I investigate further, I think it has something to do also with Edge having its dark theme enabled. High Contrast Mode does some funky stuff, and Windows is smart enough not to invert dark mode on Edge when High Contrast Mode is enabled. That is probably where the bug is coming from.