Deleting these registry keys helped me - SusClientId and SusClientIDValidation:
HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\WindowsUpdate
After rebooting the server and checking for updates again, the WSUS console status "not yet reported" disappeared and the server connection date appeared.
Deleting other keys might also help. Here's the full script:
net stop wuauserv
reg Delete HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\WindowsUpdate /v PingID /f
reg Delete HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\WindowsUpdate /v AccountDomainSid /f
reg Delete HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\WindowsUpdate /v SusClientId /f
reg Delete HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\WindowsUpdate /v SusClientIDValidation /f
net start wuauserv