Thank you for the nudge, I'm not 100% sure what could be causing this issue. I have a few suggestions below. Perhaps one of these will help. I'm also reaching out to see if I can get some help on this error.
In the Network area of the Preferences, did you make any changes to the default settings?

There is a Restore Defaults button at the bottom left hand corner of the preferences. Could you try that, apply the changes and then restart Fusion?
Some other suggestions.
Manually refresh any browser cache/options that could impact the Authentication Process:
- Close Fusion 360
- Delete the following files & folders:
- %appdata%\autodesk\neutron platform\options\{alphanumeric folder name}\NGlobalOptions.xml
- %appdata%\autodesk\neutron platform\options\NMachineSpecificOptions.xml
- %temp%\autodesk\BrowserCache folder
- %localappdata%\autodesk\web services\LoginState.xml
3. Restart Fusion 360 & Retest
Remove and/or Modify Environment Variables for HTTP or HTTPS (Windows):
1. Browse to Control Panel\All Control Panel Items\System
2. Click the Advanced System Settings link
3. In Advanced tab, select Environment Variables
4. Look for User or System variable named HTTP and HTTPS and edit or remove them.
Reset the Internet Options (Windows Only):
1. Clear the browser cache (CTRL + SHIFT + DELETE while in web browser)
2. Browse to Control Panel\All Control Panel Items\Internet Options
3. In the Advanced tab, select the Reset button to reset Internet Explorer's settings to the defaults
4. In the Security tab, select Reset All Zones to Default level
5. In the Content tab, select Clear SSL state
6. Select Apply
Toggle Proxy detection settings:
1. Browse to Control Panel\All Control Panel Items\Internet Options
2. In the Connections tab, select LAN settings
3. Try to Enable/Disable a utomatically detect settings option
3. Apply the changes and retest.
I hope these help! Please keep me posted on your progress!
Thanks,
Nathan Chandler
Principal Specialist