Word persistently can't connect to authenticate Office account ("Sorry, we are having some temporary server issues"), but Excel can

I have an Office 365 Business subscription, currently active on two machines. One of these became persistently locked out from authenticating, therefore only operating in restricted mode - the subscription was active, and working on the other machine.

The only clue as to the cause was this message any time I tried to authenticate the account (or in fact, do anything that involved connecting Word to the Office server):

Sorry, we are having some temporary server issue

It seems this is a worryingly common error, and being so vague there are many possible causes. None of the things I tried helped:

• Closing firewalls / Windows Defender temporarily and restarting the application
• Changing the network connection from 'Metered' to 'Unmetered'
• Updating Office
• Going to Control Panel > Uninstall and doing a complete repair
• Suggestions on this help forum page:
  • Resetting Internet Options via Internet Explorer's Advanced settings
  • Trying a different connection
• Looking for the registry setting described in this article (doesn't seem to exist any more)

I contacted MS Support, who suggested essentially the same things I'd already tried, but suggested a slight variant using Excel's options - and surprisingly, Excel just worked right on start up without me needing to do anything. I could authenticate my account without problems, then authenticate the device too, and this unlocked Word.

However, confusingly, Word still can't connect to the internet. It works because it knows the device is authenticated but it still won't connect to my Office account like the other applications, and gives network errors on opening as it tries and fails to load templates, scan OneDrive, etc.

What could be causing this?

This is counter-intuitive, but I got it working by disabling this option:

Word Options > Trust Center > Privacy Options

_____[ ] Let Office connect to online services from Microsoft to provide functionality that's relevant to your usage and preferences

How could disabling non-essential internet access enable essential internet access? I'm not entirely sure, but I'm guessing Word's usage logging feature had got tangled somehow - probably something similar to the case in the above-linked Angry Technician article where the connection was failing because Office was looking for a broken / non-existent / inaccessible cache.

Presumably changing this setting to turn off non-essential network traffic either flushed a broken cache, or re-routed the network traffic via some simpler, more robust route.

Following your directives it did not work instantly for me.
What I have done for this to work is to open Internet Explorer as Administrator and simple uncheck the "Automatically detect proxy settings" in the Internet Explorer Advanced Options.

Doing this, my homepage displayed immediately. It sounded good for Office 365. Bingo, my Office 365 products sign-in worked like a charm after that!