21st Century Federal Writers' Project Act This bill creates a grant program in the Department of Labor to provide eligible entities with funds to assist individuals who are unemployed or underemployed in order to document in writing and images American society and the broad impacts and effects of the COVID-19 pandemic in the United States. In addition, Labor must (1) establish a repository of works developed through the grant program in which grantees submit completed works from subgrantees, including giving credit to each writer or artist, and make such works available to the public; and (2) forward the completed work to the Library of Congress to archive such material. The Library must establish an archive program in its American Folklife Center for collection and public availability, in a digital format of such written and visual works.