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OmniSupervisorConfigProfile is the object/entity where Salesforce Omni-Channel Supervisor Configurations Profiles assignments are stored. So, we have to query the OmniSupervisorConfigProfile object/entity to fetch the Salesforce Omni-Channel Supervisor Configurations Profiles assignment.
Sample SOQL:
SELECT OmniSupervisorConfigId, OmniSupervisorConfig.DeveloperName,
ProfileId, Profile.Name
FROM OmniSupervisorConfigProfile
To query Omni-Channel Supervisor Configurations Users Assignment, please check the following: