  We calibrate a (3+1)-dimensional multistage hybrid framework using the
measured pseudo-rapidity distribution of charged particles and rapidity
distribution of net protons for central Au+Au collisions at $\sqrt{s_{\rm
NN}}=7.7,\,19.6,\,62.4,\,200$ GeV. We then study the thermodynamic properties
of the nuclear matter along the beam direction, and the phase diagram regions
probed by the hadronization process near the chemical freeze-out. Using the
rapidity-dependent thermal yields of identified particles with full rapidity
coverage from the hybrid framework, we apply different scenarios of the
statistical thermal model to extract the thermodynamic parameters at the
freeze-out, with the known system properties from the hybrid model as a closure
test. We find significant theoretical uncertainties in the thermal models when
applied to regions away from midrapidity. We also propose a thermal model
inspired by the hybrid approach that includes thermal smearing and longitudinal
flow for the nuclear matter created at low beam energies.
