We investigate the nonequilibrium dynamics of a two-dimensional rotating Bose gas confined in a symmetric anharmonic trap, employing the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We study states ranging from vortex-free configurations to multicharged (giant) vortices, prepared by tuning the rotation frequency, and analyze their response to sudden in- teraction and trap quenches. In vortex-free states, interaction quenches induce regular breathing-like dynamics, whereas in the presence of giant vortices they lead to symmetry-breaking surface excita- tions. In contrast, trap deformations that excite quadrupole-like modes produce stable oscillations in vortex-free condensates but trigger rapid, irregular, and effectively chaotic multimode dynamics in multicharged vortices. To characterize these processes beyond conventional density and phase observables, we employ information-theoretic (IT) measures, including marginal and joint spatial entropies, mutual information, and Kullback–Leibler (KL) divergence, supplemented by an angular- resolved KL measure that quantifies azimuthal density redistribution and symmetry breaking. We find that chaotic splitting is accompanied by a pronounced growth of information-theoretic indi- cators, signaling the buildup of many-body correlations and increasing complexity in the system dynamics. Our results demonstrate the extreme sensitivity of giant vortices to excitation protocols and establish IT measures as quantitative global diagnostics that complement conventional observ- ables by characterizing spatial redistribution and correlations during complex vortex dynamics.