Southeast Asian Deportation Relief Act of 2023 This bill prohibits the detention or removal of certain nationals of Vietnam, Cambodia, or Laos. Specifically, this protection from detention or removal shall apply to nationals of these countries who (1) entered the United States on or before January 1, 2008, (2) have continuously resided in the United States since entry, and (3) are subject to a final order of removal. Such individuals shall also receive employment authorization. The bill also directs the Department of Justice to grant motions to reconsider or reopen the case of any non-U.S. national who was ordered removed, deported, or excluded from the United States between April 24, 1996, and this bill's enactment and who otherwise satisfies the requirements for protection from detention or removal under this bill. For these individuals, the bill also waives certain requirements that typically apply to motions to reconsider or reopen, such as deadlines for filing such a motion. Further, the Department of Homeland Security must provide individuals covered by the bill with notice of the bill's provisions. The notice must include instructions for filing a motion to reconsider and reopen removal proceedings.