Export or Query Service Cloud Console (Console for Service) Enabled Users Using Data Loader or Developer Console.

The following resolution steps cover two scenarios: querying users with the Service Cloud User license (Console for Service) and querying users with the Console for Sales permission set.

Query Users with Service Cloud User License (Console for Service)

The field on the Salesforce User object that stores the "Service Cloud User" checkbox value is UserPermissionsSupportUser.
To export a list of users with the Service Cloud User checkbox enabled, use Data Loader Export or Developer Console with the following approach:
In Data Loader, select Export, check "Show all Salesforce objects," select the User object, and add the filter condition where UserPermissionsSupportUser equals True. Select the Id, Username, and IsActive fields along with any other desired fields. Click Finish to export the results to a CSV file.
For reference, see the Export Data documentation for full Data Loader export steps.
In Developer Console, open the Query Editor and run a SOQL query against the User object filtering where UserPermissionsSupportUser equals True. For example, query the FirstName, LastName, Id, UserPermissionsSupportUser, and IsActive fields for all users where UserPermissionsSupportUser is True.
Note: The UserPermissionsSupportUser field is not available when you use the Data Export Service to export backup data from Salesforce.

Query Users with Console for Sales Permission Set

Unlike Console for Service, which is assigned via the Service Cloud User checkbox on the User record, Console for Sales permissions are assigned via Permission Sets. To get a list of users assigned to the Console for Sales permission set, query or export from the PermissionSetAssignment object in Data Loader or Developer Console. See the Assign the Salesforce Console User Permission Set to Sales Console Users documentation for the specific permission set name to filter on.
If your organization would like the ability to report on Service Users added natively in reports, consider voting for the Idea: Gain the ability to report on Live Agent and Service users.