Advances in the research of interactions between ultrafast free electrons and light have introduced a previously unknown kind of quantum matter, quantum free-electron wavepackets(1-5). So far, studies of the interactions of cavity-confined light with quantum matter have focused on bound electron systems, such as atoms, quantum dots and quantum circuits, which are considerably limited by their fixed energy states, spectral range and selection rules. By contrast, quantum free-electron wavepackets have no such limits, but so far no experiment has shown the influence of a photonic cavity on quantum free-electron wavepackets. Here we develop a platform for multidimensional nanoscale imaging and spectroscopy of free-electron interactions with photonic cavities. We directly measure the cavity-photon lifetime via a coherent free-electron probe and observe an enhancement of more than an order of magnitude in the interaction strength relative to previous experiments of electron-photon interactions. Our free-electron probe resolves the spatiotemporal and energy-momentum information of the interaction. The quantum nature of the electrons is verified by spatially mapping Rabi oscillations of the electron spectrum. The interactions between free electrons and cavity photons could enable low-dose, ultrafast electron microscopy of soft matter or other beam-sensitive materials. Such interactions may also open paths towards using free electrons for quantum information processing and quantum sensing. Future studies could achieve free-electron strong coupling(6,7), photon quantum state synthesis(8) and quantum nonlinear phenomena such as cavity electro-optomechanics(9).