That’s what worked for me to make news disappear from the search screen - took the steps in post #14. Took me a couple minutes to figure it out.
iPhone 6S+ btw.
I think what’s key to remember about those news links Siri uses are preselected by Apple/Siri.
From what I tried in the News App settings about links/sources, etc. nothing makes any difference to the Siri Search and Suggestions swipe. They seem to be like the OP snapshot (the sources).