Electric anapoles, arising from the destructive interference of primitive and toroidal electric dipole moments, have recently emerged as a fundamental class of non-scattering sources. On the other hand, super-scattering states represent the opposite regime wherein the scattering cross-section of a subwavelength particle exceeds the single-channel limit, leading to a strong scattering behavior. Here, we demonstrate that the interplay between the topology of light and the subwavelength scatterer can lead to these two opposite responses within an isolated all-dielectric meta-atom. In particular, we present the emergence of a new non-scattering state, referred to as hybrid anapole, which surpasses conventional electric dipole anapoles by achieving a remarkable 23-fold enhancement in the suppression of far-field radiation and almost threefold enhancement in the confinement of electromagnetic energy inside the meta-atom. We also explore the role of particle orientation and its inversion symmetry in the scattering response and predict the possibility of switching between non-scattering and super-scattering states within the same platform. The presented study elucidates the role of light and matter topologies in the scattering response of subwavelength meta-atoms, uncovering two opposite regimes of light-matter interaction and opening new avenues in applications such as nonlinear optics and spectroscopy.