  In the era of gravitational wave astronomy, radial oscillations hold
significant potential for not only uncovering the microphysics behind the
internal structure but also investigating the stability of neutron stars (NSs).
We start by constructing families of static NSs following nucleonic,
quarkyonic, and hybrid equations of state and then subject them to radial
perturbations in order to explore the stability of these stars. Unlike other
literature where the fluid elements are assumed to be in chemical equilibrium,
we consider the out-of-equilibrium effects on the chemical composition of fluid
elements for the calculation of radial modes. Taking these considerations into
account, we observe that the sound speed ($c^2_s$) and adiabatic index
($\gamma$) avoid singularities and discontinuities over the equilibrium case.
We elucidate the response of the fundamental radial modes by examining the
out-of-equilibrium matter distribution scenario, offering insights into its
dynamic variations. We also demonstrate that this approach extends the stable
branches of stellar models, enabling stars to sustain stable higher-order mass
doublets, shedding some light on observation and existence of PSR J0740+6620.
