Stop COVID-19 Test Surprise Medical Bills Act of 2021 This bill modifies provisions requiring health insurance plans to cover COVID-19 diagnostic testing services at no cost, without prior authorization, and without medical management requirements. This includes the rates at which insurance plans must reimburse providers of such tests. The bill also requires the Department of Health and Human Services (HHS) to survey and report on the cash prices of testing services and the compliance of providers with the requirement to publish the prices of tests. Additionally, HHS, jointly with the Department of the Treasury and the Department of Labor, must issue guidance clarifying the process for submitting claims for testing services.