  Superconductivity (SC) is a ubiquitous feature of graphite allotropes, having
been observed in Bernal bilayers[1], rhombohedral trilayers[2], and a wide
variety of angle-misaligned multilayers[3-6]. Despite significant differences
in the electronic structure across these systems, supporting the graphite layer
on a WSe$_2$ substrate has been consistently observed to expand the range of SC
in carrier density and temperature[7-10]. Here, we report the observation of
two distinct superconducting states (denoted SC$_1$ and SC$_2$) in Bernal
bilayer graphene with strong proximity-induced Ising spin-orbit coupling.
Quantum oscillations show that while the normal state of SC$_1$ is consistent
with the single-particle band structure, SC$_2$ emerges from a nematic normal
state with broken rotational symmetry. Both superconductors are robust to
in-plane magnetic fields, violating the paramagnetic limit; however, neither
reach fields expected for spin-valley locked Ising superconductors. We use our
knowledge of the Fermi surface geometry of SC$_1$ to argue that
superconductivity is limited by orbital depairing arising from the imperfect
layer polarization of the electron wavefunctions. Finally, a comparative
analysis of transport and thermodynamic compressibility measurements in SC$_2$
shows that the proximity to the observed isospin phase boundaries, observed in
other rhombohedral graphene allotropes, is likely coincidental, constraining
theories of unconventional superconducting pairing mechanisms in theses
systems.
