Public Banking Act of 2023 This bill allows for the federal charter of public banks (i.e., banks that are wholly owned and controlled by a state, tribe, or local government). Under the bill, the Board of Governors of the Federal Reserve System must charter public banks or recognize non-federally chartered banks if they meet certain criteria. These public banks are eligible for membership in the Federal Reserve System. The Federal Reserve must offer specified services to member public member banks, including grants, payment accounts, digital dollar services, and facilities for credit, loans, and liquidity. These public banks must have a democratic governance structure, establish an environmental policy, and comply with certain lending policies. For example, these public banks must require that loan recipients do not oppose or resist unionization efforts involving projects that utilize public funds. Public banks under the bill are also prohibited from providing financial services to certain companies, including those that (1) support specified industries such as gun manufacturers or fossil fuel producers; (2) have unfair or unsafe labor practices; or (3) have a history of tax avoidance. The bill also requires the establishment of a regulatory framework for the federal recognition of securities issued by public banks. The Federal Deposit Insurance Corporation must provide unlimited deposit insurance to federally recognized public banks. The United States Postal Service must partner with these public banks to provide account and payment services at post offices.