Thanks for posting in Q&A.
1.For the critical state of the SMS_WSUS_SYNC_MANAGER, could we check wsyncmgr.log on the site server to see if the synchronization is good?
2.For the critical state of the SMS_WSUS_CONTROL_MANAGER,could we check the WSUSCtrl.log on our site server to see whether the WSUS is healthy or not?
3.For the critical state of the SMS_WSUS_CONFIGURATION_MANAGER ,may we check the WCM.log on our site server to see if the SUP configuration and connections with our WSUS server is good?
4. Also,may we try to see if we could successfully open the WSUS console?
Hope this could help you.
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