  Quantum oscillations originating from the quantization of the electron
cyclotron orbits provide ultrasensitive diagnostics of electron bands and
interactions in novel materials. We report on the first direct-space nanoscale
imaging of the thermodynamic magnetization oscillations due to the de Haas-van
Alphen effect in moir\'e graphene. Scanning by SQUID-on-tip in Bernal bilayer
graphene crystal-axis-aligned to hBN reveals abnormally large magnetization
oscillations with amplitudes reaching 500 {\mu}_B/electron in weak magnetic
fields, unexpectedly low frequencies, and high sensitivity to the superlattice
filling fraction. The oscillations allow us to reconstruct the complex band
structure in exquisite detail, revealing narrow moir\'e bands with multiple
overlapping Fermi surfaces separated by unusually small momentum gaps. We
identify distinct sets of oscillations that violate the textbook Onsager Fermi
surface sum rule, signaling formation of exotic broad-band particle-hole
superposition states induced by coherent magnetic breakdown.
