Context. On 2020 November 29, an eruptive event occurred in an active region located behind the eastern solar limb as seen from Earth. The event consisted of an M4.4 class flare, a coronal mass ejection, an extreme ultraviolet (EUV) wave, and a white-light (WL) shock wave. The eruption gave rise to the first widespread solar energetic particle (SEP) event of solar cycle 25, which was observed at four widely separated heliospheric locations (∼230°). Aims. Our aim is to better understand the source of this widespread SEP event, examine the role of the coronal shock wave in the wide distribution of SEPs, and investigate the shock wave properties at the field lines magnetically connected to the spacecraft. Methods. Using EUV and WL data, we reconstructed the global three-dimensional structure of the shock in the corona and computed its kinematics. We determined the magnetic field configurations in the corona and interplanetary space, inferred the magnetic connectivity of the spacecraft with the shock surface, and derived the evolution of the shock parameters at the connecting field lines. Results. Remote sensing observations show formation of the coronal shock wave occurring early during the eruption, and its rapid propagation to distant locations. The results of the shock wave modelling show multiple regions where a strong shock has formed and efficient particle acceleration is expected to take place. The pressure/shock wave is magnetically connected to all spacecraft locations before or during the estimated SEP release times. The release of the observed near-relativistic electrons occurs predominantly close to the time when the pressure/shock wave connects to the magnetic field lines or when the shock wave becomes supercritical, whereas the proton release is significantly delayed with respect to the time when the shock wave becomes supercritical, with the only exception being the proton release at the Parker Solar Probe. Conclusions. Our results suggest that the shock wave plays an important role in the spread of SEPs. Supercritical shock regions are connected to most of the spacecraft. The particle increase at Earth, which is barely connected to the wave, also suggests that the cross-field transport cannot be ignored. The release of energetic electrons seems to occur close to the time when the shock wave connects to, or becomes supercritical at, the field lines connecting to the spacecraft. Energetic protons are released with a time-delay relative to the time when the pressure/shock wave connects to the spacecraft locations. We attribute this delay to the time that it takes for the shock wave to accelerate protons efficiently.