Unfortunately, there is not an Out-of-the-box broker/smartobject that would return this information that you are seeking. But I believe this can be done with custom code/customer broker.
If a task is assigned to a role, but WITHOUT the "Plan Per Destination" setting "Resolve all roles and groups to users." I believe you can only retrieve this information through the "SourceCode.Workflow.Client" API using perhaps the "worklistItem.Status" field. This will most likely involve determining the users in the role first, then looping through each of the users in the role calling their "SourceCode.Workflow.Client" > OpenWorklist() to retrieve the task and the current worklist item status of that their task.
If a task is assigned to a role, but WITH the "Plan Per Destination" setting "Resolve all roles and groups to users." you can use the "SourceCode.Workflow.Client" similar to Option 1.
But it may also be possible to return this information from the "SourceCode.Workflow.Management" API > using the Global Worklist similarly to:
This would be similar to the data that is available in the K2 Workspace > Wokflow Server > Global Worklist, when using the "Plan Per Destination" setting "Resolve all roles and groups to users." option.
Perhaps the K2 Market Worklist Broker and Management Worklist broker can also provide a starting point/smartobject to do so:
Please know that K2 Market solution are non-tested/supported by K2 Support. But perhaps K2 Remote Services/K2 Community site can provided additional guidance/best practices.