Primacy Certainty Act of 2023 This bill modifies provisions of the underground injection control program established under the Safe Drinking Water Act related to the review of state applications to obtain responsibility for regulating Class VI wells, which are used to store captured carbon. The bill sets forth a process to give states primary enforcement responsibility for such wells if the Environmental Protection Agency (EPA) fails to meet specified deadlines. In addition, the bill prohibits the EPA from conditioning the approval of state applications on the inclusion of provisions that are not included in the applications or not explicitly required by the Safe Drinking Water Act.