We study the formation of magnetic clusters in frustrated magnets in their cooperative param-agnetic region. For this purpose, we consider the J1-J2-J3 classical Heisenberg model on kagome and pyrochlore lattices with J2 = J3 = J. In the absence of farther-neighbor couplings, J = 0, the system is in the Coulomb phase with magnetic correlations well characterized by pinch-point singularities. Farther-neighbor couplings lead to the formation of magnetic clusters, which can be interpreted as a counterpart of topological-charge clusters in Ising frustrated magnets [T. Mizoguchi, L. D. C. Jaubert and M. Udagawa, Phys. Rev. Lett. 119, 077207 (2017)]. Reflecting the tendency of clustering, the static and dynamical magnetic structure factors, respectively S(q) and S(q, ω), develop half-moon patterns. As J increases, the continuous nature of the Heisenberg spins enables the half-moons to coalesce into connected " star " structures spreading across multiple Brillouin zones. These characteristic patterns are complementary of pinch point singularities, and signal the proximity to a Coulomb phase. Shadows of the pinch points remain visible at finite energy, ω. This opens the way to observe these clusters through (in)elastic neutron scattering experiments. The origin of these features are clarified by complementary methods: large-N calculations, semi-classical dynamics of the Landau-Lifshitz equation, and Monte Carlo simulations. As promising candidates to observe the clustering states, we revisit the origin of " spin molecules " observed in a family of spinel oxides AB2O4 (A = Zn, Hg, Mg, B = Cr, Fe).< Réduire