There are two chambers of Congress, so why would it be only the House? There are three voting members of the governing board, only one of them did Pelosi even vote on.
She does not have a sergeant-at-arms, the House does. The Senate has another sergeant-at-arms. She has no day-to-day say over any of this.
She is one of 435 people who voted for one third of the governing oversight of the Capitol Police. trump directly nominated one third of the governing oversight of the Capitol Police. And McConnell was one of 100 people who both confirmed trump nomination, and elected the last third of the governing oversight of the Capitol Police.
You are stuck using a citation that says you are "mostly wrong".