Computational modeling of the heart has emerged as a pivotal tool for advancing cardiovascular research. However, the high computational cost of whole-heart modeling, which involves coupling multi-physics and multi-scale phenomena, poses significant challenges. This study focuses on cardiac electrophysiology simulations based on the monodomain system of equations coupled to ionic models. These simulations demand high spatial and temporal resolution due to the sharp and fast propagating wavefronts of electrical signal in cardiac tissue. While classical approaches use linear finite elements on fine grids, higher-order finite elements and Discontinuous Galerkin (DG) methods have recently gained traction. Polytopal methods are particularly appealing in this context, as they allow coarse grids to be easily constructed by merging polygonal and polyhedral elements. However, developing automated, high-quality agglomeration strategies for such elements remains a challenging and unresolved problem. Preserving the quality of the original mesh is essential, as any degradation could negatively impact the method's stability and accuracy. This work leverages a polytopic DG framework to develop multilevel preconditioners for the monodomain model with polynomial degrees p≥1. We exploit a robust, automated, and dimension-independent coarsening strategy based on R-trees, enabling the creation of nested, high-quality agglomerated grids. The resulting nested hierarchy of meshes is used within a multigrid framework to precondition DG discretizations. We present numerical experiments on 2D and 3D geometries, to evaluate performance across various numerical settings. These experiments are implemented using a new C++ library built on the deal.II Finite Element library, showcasing efficient parallel capabilities.