Katie Couric feels nothing but empathy and respect for Brooke Nevils, who accused Matt Lauer of raping her. The former “Today” show co-host, 69, told Page Six that she has not read Nevils’ memoir, “Unspeakable Things: Silence, Shame and the Stories We Choose to Believe,” but did “read an excerpt.” “I feel terrible for her,” Couric said at the City Harvest Presents The 2026 Gala: Shaken, Not Stirred. “I think she’s very brave to write the book.” Katie Couric spoke to Page Six on Tuesday at a City Harvest gala. Getty Images Couric shared that she felt terribly for Brooke Nevils, who alleged that Couric’s former “Today” show co-anchor had raped her. Robert Miller Lauer’s lawyer did not reply to Page Six’s request for comment. Lauer and Couric worked together as co-anchors on the “Today” show for nearly a decade, from 1997 to 2006. Couric had long left the show before Lauer was unceremoniously axed in 2017 following accusations of sexual misconduct.…