We investigate s-wave $K^{-}$ condensation in dense matter and neutron stars within the updated Chiral Mean Field model with an improved meson description (mCMF), which incorporates dynamically generated in-medium meson masses. In contrast to conventional relativistic mean-field approaches with fixed meson masses, this framework introduces a self-consistent feedback between the meson sector and the dense-matter equations of motion. The kaon dispersion relation is derived from the nonlinear SU(3) Lagrangian including Weinberg–Tomozawa and additional baryon–pseudoscalar interactions, and the onset of condensation is determined under $\beta$ equilibrium and charge neutrality. We analyze the impact of hyperons, muons, and kaon condensation on the equation of state, on neutron-star mass–radius relations, and neutron-star thermal evolution, and examine the sensitivity of the onset density and stellar properties to variations in the nucleon–kaon scattering length and to different model vector parameters and vector self-interactions. We find that $K^{-}$ condensation sets in between $n\sim (2-8)n_0$ (in units of nuclear saturation density) and leads to a moderate to strong softening (in one case, a slight stiffening of the equation of state), depending on the interplay with hyperons and the strength of kaon–nucleon interactions, while remaining compatible with current $2M_{\odot }$ and small-radius neutron-star observational constraints and producing distinguishable behavior in the neutron-star cooling. This work provides an improved and thermodynamically consistent framework for studying exotic degrees of freedom in neutron-star matter.