Stop COVID-19 Test Surprise Medical Bills Act of 2021 This bill modifies provisions requiring health insurance plans to cover COVID-19 (i.e., coronavirus disease 2019) diagnostic testing services at no cost, without prior authorization, and without medical management requirements. The bill specifies that a plan may not make determinations about the circumstances surrounding individuals' tests, such as why they sought testing or whether they showed symptoms of COVID-19. The bill also specifies that plans may encourage individuals to obtain tests from lower priced providers as long as such efforts do not delay, or impede access to, testing. 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 such prices. 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.