  We carry out a theoretical study of unconventional superconductivity in
twisted bilayer cuprates as a function of electron density and layer twist
angle. The bilayer $t$-$J$-$U$ model is employed and analyzed within the
framework of a generalized variational wave function approach in the
statistically-consistent Gutzwiller formulation. The constructed phase diagram
encompasses both gapless $d$-wave state (reflecting the pairing symmetry of
untwisted copper-oxides) and gapped $d+\mathrm{e}^{i\varphi}d$ phase that
breaks spontaneously time-reversal-symmetry (TRS) and is characterized by
nontrivial Chern number. We find that $d+\mathrm{e}^{i\varphi}d$ state occupies
a non-convex butterfly-shaped region in the doping vs. twist-angle plane, and
demonstrate the presence of previously unreported reentrant TRS-breaking phase
on the underdoped side of the phase diagram. This circumstance supports the
emergence of topological superconductivity for fine-tuned twist angles away
from $45^\circ$. Our analysis of the microscopically derived Landau free energy
functional points toward sensitivity of the superconducting order parameter to
small perturbations close to the topological state boundary.
