Promoting Access to Credit for Homebuyers Act of 2021 This bill requires Freddie Mac, Fannie Mae, and the Department of Housing and Urban Development to purchase or insure single-family mortgages originated on or after February 1, 2020, on the same terms as they otherwise would despite a borrower entering into, or inquiring about, forbearance due to a COVID-19 (i.e., coronavirus disease 2019) related hardship. This requirement begins 5 days after enactment of this bill and ends 60 days after the end of the period of time a borrower may request a COVID-19 related forbearance. The Federal Housing Finance Agency may not increase fees or otherwise restrict access to credit during the COVID-19 emergency without congressional notice. The Government Accountability Office must report on COVID-19-related assistance to consumers by Freddie Mac, Fannie Mae, and the Federal Housing Administration mortgage insurance programs.