  Within the framework of extended black hole thermodynamics, where the
cosmological constant acts as the thermodynamic pressure and its conjugate as
the thermodynamic volume, we analyze the phase structure and thermodynamic
geometry of the three-dimensional quantum-corrected BTZ (qBTZ) black hole. Our
results uncover two-phase transitions in the $T-S$ plane across all pressures
except at a critical value. Numerical analysis reveals continuous critical
phenomena along the coexistence curve, with critical exponents of 2 and 3 for
the heat capacity at constant pressure and the NTG curvature, respectively.
Importantly, these values notably deviate from the well-known critical
exponents observed in mean-field Van der Waals (VdW) fluids, where the NTG
curvature and heat capacity demonstrate discontinuous criticality. To our
knowledge, our investigation is the first exploration of critical behavior in
black holes incorporating consistent semiclassical backreaction.
