Surface Transportation Extension Act of 2021 This bill extends and revises provisions related to federal-aid highway, transit, highway safety, rail, and other surface transportation programs of the Department of Transportation (DOT). Among other provisions, the bill extends FY2021 enacted levels of funding through October 31, 2021, for federal-aid highway, transit, and safety programs; increases the cap from $600 million to $700 million on the amount of funding for nationally significant freight and highway projects and extends authority through FY2022 for DOT to provide funding for such projects; revises and extends authority through FY2022 for the National Highway Traffic Safety Administration to carry out collaborative research on in-vehicle technology to prevent alcohol-impaired driving; extends authority through October 31, 2021, for DOT to provide direct loans and loan guarantees for railroad rehabilitation and development near rail stations; reauthorizes and extends authority through FY2022 for the Appalachian Regional Commission; compensates any federal employee who is furloughed or required to work without pay during the authorization lapse in Highway Trust Fund expenditure authority at the earliest possible date after the lapse ends; and extends expenditure authority through November 1, 2021, for the Highway Trust Fund, Sport Fish Restoration and Boating Trust Fund, and the Leaking Underground Storage Tank Trust Fund.