Civil Nuclear Export Act of 2023 This bill provides the Export-Import Bank with certain authorities to finance nuclear exports. Specifically, the bill allows the Export-Import Bank to provide financing for liquid metal fast breeder nuclear reactors and nuclear fuel reprocessing facilities if they are otherwise permitted by law. Additionally, the bill expands the China and Transformational Exports Program (CTEP) by making nuclear facilities eligible for financing under the program. Currently, the bank may extend loans, guarantees, and insurance to advance the comparative leadership of the United States with respect to China in specified export areas (e.g., artificial intelligence, biotechnology, and wireless communications equipment). This bill expands those areas to include civil nuclear facilities, materials, technologies and related goods and services that support the development of an effective nuclear energy sector. The bill also revises the financial limitation on the outstanding aggregate amount of all of the bank's loans, guarantees, and insurance. In particular, the bill exempts those amounts attributed by the bank to CTEP, as long as that financing does not exceed a specified amount. The bill also increases from 2% to 4% the bank's default rate cap. Further, the bill allows the bank to exclude financing under CTEP from this default rate, subject to approval of the bank's board of directors. The bill establishes liability limits for damages that are caused by nuclear projects financed by the bank.