The COVID-19 Hospital and Health Provider Loan Conversion Act of 2021 This bill establishes and otherwise modifies requirements for the Medicare Accelerated and Advance Payment Program during the public health emergency relating to COVID-19 (i.e., coronavirus disease 2019). The program provides Medicare payments in advance to eligible providers experiencing claims or cash flow disruptions, such as during national emergencies; the program was specifically expanded in response to COVID-19 to encompass more types of providers, subject to certain recoupment and repayment provisions. The bill requires the Centers for Medicare & Medicaid Services to waive recoupment and repayment for providers who meet specified requirements. Among other criteria, providers must not have engaged in surprise billing practices with respect to COVID-19 patients. Providers must still repay any amounts not used for COVID-19 expenses; the bill caps the interest rate on such repayments at 2% upon a demonstration of hardship. The bill also requires private health insurers to treat out-of-network COVID-19 services as in-network for purposes of payment and cost-sharing.