@Dinesh Prajapati Hello and welcome to Microsoft Q&A.
I understand you wish to monitor and enable the "Interactive Authoring" feature in Data Factory.
Even if this is possible, I don't think it is advisable. Interactive Authoring features are for when someone is working on the Factory. Keeping it active while the engineer sleeps does not help.
Since the api for interactive authoring is not part of the user documentation, it is not a supported scenario. Given the browser makes the call to enable interactive authoring, it is theoretically possible for you to do as well. 'Not supported' means I can't help you all the way. You assume any expenses or risk.
So, with the disclaimer out of the way, I see the browser makes a PUT call to
https://management.azure.com/subscriptions/{subscriptionId}/resourceGroups/{resourceGroupName}/providers/Microsoft.DataFactory/factories/{factoryName}/integrationRuntimes/{integrationRuntimeName}/enableInteractiveQuery?api-version=2018-06-01
With a body of
{"autoTerminationMinutes":60}
Whether the interactive authoring is currently enabled or not, is part of the ...integrationruntimes/{IntegrationRuntimeName}/getStatus?api-version=2018-06-01
under $.properties.typeProperties.interactiveQuery.status