Meanwhile, I’d like to confirm whether you can sign into the Office 2016 applications with another work and school account. If yes, untick it, restart the Mac and do a test to see the result. I suggest you open System Preferences>Network>Advanced>check if the Auto Proxy Discovery is ticked.
I have already contacted Microsoft Office support and they replied ' From the error message, it sounds like a network issue. It appears the message 'No network connection - Please check your network settings and try again.' even if I am fully connected.
I am not able to sign in from my computer to any of the Office applications (while I can from my smartphone).
