Error from WUHandler.log:

Its a WSUS Update Source type ({B4F31904-A2D1-411C-AF25-9C68F7969A31}), adding it.
Existing WUA Managed server was already set (http://<SOMESERVER>:8530), skipping Group Policy registration.
Added Update Source ({B4F31904-A2D1-411C-AF25-9C68F7969A31}) of content type: 2
Async searching of updates using WUAgent started.
Async searching completed.
OnSearchComplete – Failed to end search job. Error = 0x8024401b.
Scan failed with error = 0x8024401b.

Error from WindowsUpdates.log:

1284 804 PT WARNING: GetConfig failure, error = 0x8024401B, soap client error = 10, soap error code = 0, HTTP status code = 407
1284 804 PT WARNING: PTError: 0x8024401b
1284 804 PT WARNING: GetConfig_WithRecovery failed: 0x8024401b
1284 804 PT WARNING: RefreshConfig failed: 0x8024401b
1284 804 PT WARNING: RefreshPTState failed: 0x8024401b
1284 804 PT WARNING: PTError: 0x8024401b
1284 804 Report WARNING: Reporter failed to upload events with hr = 8024401b.

Solution:

And this is wierd!

Change the site system FQDN to lowercase (Site Database -> Site Management -> Central Site -> Site Settings -> Site Systems -> <siteserver> -> ConfigMgr Site System)

Restart the Windows Update Service on the client computer

Initiate the Software Update Scan Cycle and you are go!