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:

How to query Salesforce Omni-Channel Supervisor Configurations Users Assignment?