Protect Seniors and Cut Waste Act This bill prohibits the budgetary effects of the American Rescue Plan Act of 2021 from being counted for the purposes of determining whether a specified sequester occurs under the Statutory Pay-As-You-Go Act of 2010. (The American Rescue Plan Act of 2021 provided funding to address the impact of COVID-19. Sequestration is a process of automatic, usually across-the-board spending reductions under which budgetary resources are permanently cancelled to enforce specific budget policy goals.) The bill also modifies several other provisions related to COVID-19 spending. Among other modifications, the bill provides supplemental appropriations for the Public Health and Social Services Emergency Fund to reimburse certain health care providers for health care related expenses or lost revenues that are attributable to the coronavirus; rescinds certain funds that were provided for payments to states, territories, and tribal governments to mitigate the fiscal effects stemming from the COVID-19 public health emergency; prohibits individuals who are incarcerated or unlawfully present in the United States from receiving 2021 recovery rebates; and rescinds funds that were provided by the American Rescue Plan Act of 2021 for the National Endowment for the Arts, the National Endowment for the Humanities, and the Emergency Federal Employee Leave Fund.