set workflow status action

The set workflow Status action only updates the the status on the item it is run on, not on a task items that may be generated by the workflow.
You would need to use an update item action to specifically update a column in the task list to acheive this funtionality.

Hi,

"using the action set workflow status to set custom string value in each step in the workflow"
So you have the status, now update a column for the task with the same status.

https://help.nintex.com/en-US/nintex2016/4.5.2/#cshid=NintexWorkflowSetCustomWorkflowStatus

Updates the status of the workflow instance as shown on the Workflows page and, for list workflows, in the workflow status column within the list.

You can use this action to track workflow status during the progress of the workflow instance, assigning either standard or custom workflow status values. Standard workflow status values include "In Progress," "Canceled," "Completed," and "Errored."​

The value is not stored anywhere. You will need to create a variable and store the value if you would like to use it on you task list.