NOAA Weather Radio Modernization Act of 2023 or the NWR Modernization Act of 2023 This bill requires the National Oceanic and Atmospheric Administration (NOAA) to expand and enhance the NOAA Weather Radio All Hazards (NWR), which is a nationwide network of radio stations that broadcast continuous weather information from the National Weather Service. NOAA must expand coverage of the NWR and ensure its reliability by maintaining support for systems that serve areas that lack or have poor quality cellular service; ensuring consistent maintenance of broadcast equipment; strengthening the ability of the NWR to amplify non-weather emergency messages; and acquiring additional transmitters to expand coverage to rural and underserved communities, national parks, and recreation areas. NOAA must also assess methods for enhancing the NWR, such as broadcasting continuously and in real time and making the NWR compatible with third-party platforms (e.g., websites and mobile applications). Prioritizing recommendations from the assessment, NOAA must further enhance the NWR, including by (1) upgrading telecommunications infrastructure to expedite the transition to internet-based broadcasts, and (2) researching means to transmit NWR signals to remote transmitters or those that do not have internet capabilities.