Structural phase transitions drive several unconventional phenomena including some illustrious ferroic attributes which are relevant for technological advancements. With this note, we have investigated the structural transition of perovskite-type trigonal Ba2ZnTeO6, across Tc ~ 150 K, which is also accompanied by a para- to ferroelastic transition. With the help of Raman spectroscopy and density-functional theory (DFT)-based calculations, here we report new intriguing observations associated with the phase transition in Ba2ZnTeO6 elucidating the lattice dynamics across the Tc. We have observed the presence of a central peak (quasi-elastic Rayleigh profile), huge softening in the soft mode, hysteretic phonon behavior, and signatures of coexistent phases. The existence of a central peak in Ba2ZnTeO6 is manifested by a sharp rise in the intensity of the Rayleigh profile in concomitant with the damping of the soft mode near Tc, shedding light on the lattice dynamics during the phase transition. While most of the phonon bands split below Tc confirming the phase transition, we have observed thermal hysteretic behavior of phonon modes that signifies the first-order nature of the transition and presence of coexisting phases, which are corroborated by our temperature-dependent x-ray diffraction and specific heat measurements. Further, an evidence of the concomitant structural transition appears in the form of huge softening in the thermal response of the soft phonon mode at ~ 31 cm-1 which is remarkable compared to the hitherto known behavior of soft modes in well-known ferroelectrics. This is further corroborated by our phonon calculations that show an unstable Eg-mode in the high-symmetry structure involving TeO6 octahedral rotation (with Ba and Zn translation) which later condenses into the C2/m low-symmetry phase.