The Large Hadron Collider at CERN will undergo an upgrade in order to increase its luminosity to 7.5 × 10³⁴ cm^-2s^-1. The increased luminosity during this High-Luminosity running phase, starting around 2029, means a higher rate of proton-proton interactions, hence a larger ionizing dose and particle fluence for the detectors. The current tracking system of the CMS experiment will be fully replaced in order to cope with the new operating conditions. Prototype planar pixel sensors for the CMS Inner Tracker with square 50 μm × 50 μm and rectangular 100 μm × 25 μm pixels read out by the RD53A chip were characterized in the lab and at the DESY-II testbeam facility in order to identify designs that meet the requirements of CMS during the High-Luminosity running phase. A spatial resolution of approximately 3.4 μm (2 μm) is obtained using the modules with 50 μm × 50 μm (100 μm × 25 μm) pixels at the optimal angle of incidence before irradiation. After irradiation to a 1 MeV neutron equivalent fluence of Φ_eq = 5.3 × 10¹⁵ cm^-2, a resolution of 9.4 μm is achieved at a bias voltage of 800 V using a module with 50 μm × 50 μm pixel size. All modules retain a hit efficiency in excess of 99% after irradiation to fluences up to 2.1 × 10¹⁶ cm^-2. Further studies of the electrical properties of the modules, especially crosstalk, are also presented in this paper.