The recent discovery of two-dimensional (2D) van der Waals magnets is a crucial turning point in the quantum magnet research field, since quantum fluctuations and experimental difficulties often elude stable magnetic orders in two dimensions. This opens new doors to delve for novel quantum and topological spin configurations, which may or may not have direct analogs in bulk counterparts. Here we study a twisted bilayer geometry of 2D magnets in which long-range spin-spin interactions naturally commence along the interlayer Heisenberg (T-perpendicular to) and dipole-dipole (J(D)) channels. The J(perpendicular to)-J(D) parameter space unveils a hierarchy of distinct skyrmion phases, including point-, rod-, and ring-shaped topological charge distributions. Furthermore, we predict a topological antiferroelectric phase, where oppositely charged antiskyrmion pairs are formed, and the corresponding topological dipole moments become ordered in a Neel-like state-hence dubbed the topological antiferroelectric state. The results indicate that the twisted magnetic layer provides a versatile setting to engineer and tune a plethora of skyrmion phases and their dynamics.