You can now slice and dice your Google Search Console Performance report by news content versus web, image or video content. Google just added a new filter under the performance report "search type" option for "News."
Here is a screen shot of this filter:
Google announced this on Twitter saying " Now you can analyze traffic coming from the News tab on Google Search. Learn more about filtering data on Performance reports."
Here is the help document with more details including that this news filter only shows you impressions and clicks from the Google News tab (not necessarily the top stories carousel).
Note, this data started to fill on June 30, 2020 based on what I see in my performance report.
Forum discussion at Twitter.
Update: Now Google is sending email to those with news traffic of the new News filter. It says "Google Search News tab data now in Search Console Performance report. We've recently added new data to the Performance report in Search Console: Google Search's News tab data. This data shows clicks, impressions, and click-through rate for any links seen in the "News" tab in Google Search results. To access this data in the report, click the "Search type: Web" filter on the top of the report, then select "News". For your convenience, you can also access your News search data directly by clicking the button below."
Update: Again, as I said above, this is only filtering the news tab, not top stories carousel:
FWIW "Top Stories" would be included in the normal web search setting in the performance report.
— 🍌 John 🍌 (@JohnMu) July 21, 2020