How should providers account for these funds for purposes of cost reports and similar reports?

Payments received from the program are claims reimbursements and should be treated in the same manner as reimbursements received from commercial insurance, Medicaid, and/or Medicare, including in how revenue or losses are determined. See guidance issued by the Centers for Medicare & Medicaid Services (PDF - 1 MB) on how providers should report claims reimbursed through the HRSA COVID-19 Uninsured Program on the S-10 worksheet.