State and Local Digital Service Act of 2021 This bill provides support for the establishment of digital services in state, county, local, and tribal governments. Specifically, the bill directs the General Services Administration (GSA) to establish (1) a Digital Service Grant Program to provide grants to such governments to establish or support a digital service team, and (2) a Digital Service Planning Grant Program to provide grants to create a plan to establish a digital service team. The GSA must (1) report periodically to Congress and make publicly available on its website information regarding the grants, and (2) issue guidance to streamline the procurement of federal services and technology by states, local governments, and Indian tribes.