<p>Superconductivity is a common feature of graphite allotropes, having been observed in Bernal bilayers, rhombohedral trilayers and a wide variety of angle-misaligned multilayers. Despite notable differences in the electronic structure of these systems, supporting the graphite on a WSe₂ substrate has been consistently observed to expand the range of the superconductivity in terms of carrier density and temperature. Here we report the observation of two distinct superconducting states in Bernal bilayer graphene with strong proximity-induced Ising spin–orbit coupling. Our quantum oscillation measurements show that, although the normal state of the first superconducting phase is consistent with the single-particle band structure, the second emerges from a nematic normal state with broken rotational symmetry. Both superconductors are robust to in-plane magnetic fields, but neither reach fields expected for spin–valley-locked Ising superconductors. The Fermi surface geometry of the first superconducting phase suggests that the superconductivity is limited by orbital depairing arising from the imperfect layer polarization of the electron wavefunctions. Finally, an analysis of transport and thermodynamic compressibility measurements in the second superconducting phase shows that the proximity to isospin phase boundaries, observed in other rhombohedral graphene allotropes, is probably coincidental, thus constraining theories of the pairing mechanisms in these systems.</p>