Performance-Based Public Buildings Act of 2021 This bill directs the General Services Administration to carry out a pilot program to enter into public-private partnerships to carry out projects to acquire space for public building purposes. The Government Accountability Office shall conduct a review of all such projects and submit a report to Congress that includes (1) a review and evaluation of the public-private partnerships executed and a comparison of such agreements to similar projects completed as government construction, and (2) recommendations on the use of public-private partnerships as options for meeting the space needs of the federal government.