No, the temporary federal enhancement to unemployment ($600 weekly) provided by the CARES Act is not included as annual income for Section 8 Housing Choice Voucher and Public Housing tenants. However, regular unemployment payments issued by the state that are not part of the CARES Act stimulus package are counted as income and should be reported to the housing authority.
State paid unemployment benefits have always been considered as annual income for the Housing Choice Voucher and Public Housing Programs. Temporary, non-recurring payments are not counted as annual income for those housing programs.
The Housing Choice Voucher and Public Housing federal regulation addressing excluded income can be found here. Also see page 10, Question 5 in HUD’s Questions and Answers for Multi-Family Housing Stakeholders, found here.
For information on similar questions, read: Are Section 8 tenants required to report their income from the government stimulus check?