We investigate density-induced conversion of neutrons into a neutral dark baryon $\chi$ in cold, charge-neutral and $\beta$-equilibrated neutron-star matter containing hyperons and the complete $\Delta (1232)$ quartet. The hadronic sector is described within a density-dependent covariant density-functional framework using the DDME2 parameterization. A scalar Higgs portal is also included as a possible interaction channel between the dark and hadronic sectors; its mean-field contribution is found to be numerically negligible for the couplings considered here. In the assumed chemical-equilibrium limit, the $\chi$ abundance is determined by the coupled equilibrium equations and total baryon-number conservation. We show that the appearance of hyperons and $\Delta$ resonances modifies the neutron chemical potential and delays the onset of the dark baryon, thereby reducing its abundance relative to nucleonic matter. This competition produces characteristic changes in the equation of state (EOS), particle composition, sound speed and adiabatic index. For $m_{\chi }=1250$, $1300$ and $1400$ MeV, the maximum masses of the complete $N+Y+\Delta +\chi$ configurations are found to be $1.80$, $1.90$ and $2.02M_{\odot }$, respectively, showing that the massive-pulsar constraint strongly disfavors the lighter dark-baryon benchmarks for the adopted couplings. The radial composition further indicates that, for $m_{\chi }=1400$ MeV, $\chi$ is confined to the inner core of the most massive stars, while canonical configurations remain essentially insensitive to the dark sector. The resulting stellar modifications are therefore governed predominantly by the conversion-induced rearrangement of the equilibrium composition rather than by Higgs-mediated interactions. Our results demonstrate that the interplay between conventional non-nucleonic degrees of freedom and density-generated dark baryons is crucial for assessing the astrophysical viability of such dark-sector extensions of dense matter.