Recently, representatives of the US executive branch have made statements in their official capacities, asserting that Kilmar Ábrego García is a "terrorist", a member of MS-13, and a convicted criminal. These include statements to the press by spokespeople including the Press Secretary and Attorney General, and statements in court or submitted to the court by Department of Justice lawyers.
Suppose Ábrego García would be in a position to file suit for defamation, and could show that these claims are false and damaged his reputation. Would these officials have protection against defamation claims, by some form of immunity? In particular, is there a "clearly established" right to not be defamed, which would overcome a claim of qualified immunity?