Gyrotrons are essential devices for the development of nuclear fusion, but their design and reliable operation still present numerous challenges. In particular, certain gyrotrons encounter issues related to trapped electron clouds in the magnetron injection gun (MIG) region, also known as the gyrotron electron gun, which causes undesired currents and operational failures. The complex dynamics of these electron clouds are not yet fully understood. This study validates the two-dimensional (2D) particle-in-cell code FENNECS [Le Bars et al., Comput. Phys. Commun. 303, 109268 (2024)], a numerical tool specifically developed to investigate the phenomenon of electron trapping, by comparing its numerical predictions with experimental data from the TRapped Electrons eXperiment (T-REX) [Romano et al., Rev. Sci. Instrum. 95, 103511 (2024)], an experimental setup designed to reproduce the characteristic conditions of MIGs leading to electron trapping. A comprehensive set of simulations exploring various parameters influencing the electron cloud is presented and directly compared with experimental measurements from T-REX. The study not only demonstrates strong agreement between simulations and experiments on many aspects but also highlights discrepancies. These discrepancies are attributed to the development of the diocotron instability within the electron cloud, driven by the collective azimuthal drift of the non-neutral plasma, which significantly alters its dynamics. This is a phenomenon that the code cannot account for due to its 2D axisymmetric geometry. A theoretical study based on a reduced fluid model describing the diocotron instability sheds light on the potential consequences on the electron cloud dynamics and provides explanations for the differences observed between simulations and experiments. The findings are further supported by additional experimental measurements in T-REX. This work represents a significant step forward in understanding the dynamics of trapped electron clouds in gyrotron MIGs and contributes to the ongoing effort to develop more reliable and efficient gyrotrons.