Rio San José and Rio Jemez Water Settlements Act of 2023 This bill recognizes and settles certain water rights claims in New Mexico of (1) the Pueblos of Acoma and Laguna, and (2) the Pueblos of Jemez and Zia. It also establishes and provides funding for settlement trust funds. Specifically, the bill authorizes, ratifies, and confirms a specified water rights settlement agreement entered into by the Pueblo of Acoma, the Pueblo of Laguna, the United States, New Mexico, and others, thus satisfying claims to water rights in the Rio San José Stream System in New Mexico. With respect to the water settlement for the Pueblos of Acoma and Laguna, the bill establishes and provides funding for the Pueblo of Acoma Settlement Trust Fund, the Pueblo of Laguna Settlement Trust Fund, and the Acomita Reservoir Works Trust Fund. Additionally, the bill authorizes, ratifies, and confirms a specified water rights settlement agreement entered into by the Pueblo of Jemez, the Pueblo of Zia, the United States, New Mexico, and others, thus satisfying claims to water rights in the Jemez River Stream System in New Mexico. With respect to the water settlement for the Pueblos of Jemez and Zia, the bill establishes and provides funding for the Pueblo of Jemez Settlement Trust Fund and the Pueblo of Zia Settlement Trust Fund. For both of these agreements, the bill (1) specifies the water rights of the pueblos; and (2) outlines waivers, releases, and retentions of claims by the pueblos and the United States.