Possibly a Deputy Sergeant at Arms for the House of Representatives.
They are responsible for security of the members of Congress, and for the House of Representatives part of the Capitol. The shooting took place at the entrance of the Speaker’s Lobby, which they might view as a last line of defense. The Sergeant of Arms and his deputies wear suits, and are armed.
He might possibly be Secret Service, because the Speaker is third in line to the Presidency, but I doubt that.
Did the guy who shot the woman, killing her, ever consider a warning shot?
I doubt if he was secret service, they are brilliant at non-lethal defense.