In this ArXiv preprint 2504.03842, we demonstrate a subtle competition between cavity frequency and interlayer tunneling in graphene stacks that is responsible for topological phase transitions in light-matter Hilbert space and that cannot be captured by mean-field theory in vacuum. A systematic exploration of multilayer graphene heterostructures and stacking configurations in a chiral tHz cavity reveals that linear dispersion enhances the low-energy cavity-induced topological gap.