South China Sea and East China Sea Sanctions Act of 2021 This bill authorizes sanctions on Chinese individuals and entities that participate in certain activities related to China's territorial disputes in the South China Sea and the East China Sea. The President may impose property-blocking and visa-denial sanctions on certain Chinese individuals and entities, including those that are (1) responsible for or significantly contributing to certain large-scale projects, such as reclamation and militarization projects, in the disputed parts of the South China Sea; (2) responsible for or significantly contributing to actions that inhibit another country from protecting its sovereign rights to access resources in the South China Sea; and (3) responsible for or complicit in actions that threaten the peace, security, or stability in disputed South China Sea areas or in an East China Sea area administered by Japan or South Korea. The President may also (1) deny visas to the corporate officers and controlling shareholders of sanctioned entities, (2) subject sanctioned individuals or entities to certain export restrictions, and (3) prohibit U.S. individuals and entities from investing in sanctioned entities or individuals. The Department of State must periodically submit a report to Congress identifying countries that recognize China's claims to the contested territories.