  We explore Bernal bilayer graphene in the presence of long-range Coulomb
interactions, short-range Hund's coupling, and proximity-induced Ising
spin-orbit coupling using self-consistent Hartree-Fock simulations. We show
that the interplay between these three ingredients produces an intricate phase
diagram comprising a multitude of symmetry-broken metallic states tunable via
doping and applied displacement field. In particular, we find intervalley
coherent and spin-canted ground states that may hold the key to understanding
spin-orbit-enabled superconductivity observed in this platform. We also
investigate various phase transitions where a continuous $\mathrm{U}(1)$
symmetry is broken to ascertain the possible role of critical fluctuations on
pairing.
