No Biometric Barriers to Housing Act of 2023 This bill prohibits owners of certain federally assisted rental units from using facial recognition, physical biometric recognition, or remote biometric recognition technology in any units or in any building or on any grounds containing such a unit for the purpose of surveillance or any other use that has an adverse effect on a tenant's fair access to affordable housing that is free from bias and discrimination. Within one year, the Department of Housing and Urban Development must report on any known use of such technology in federally assisted rental units in the preceding five years.