We study the evolution of matter composition from nuclear to quark densities in the confining regime by extending an ideal model of quarkyonic matter, the IdylliQ model, to multiflavor systems including strangeness. The model provides a dual description of quark and baryon occupation probabilities which are determined by minimizing the energy of the system. Saturation of low-momentum quark states drives the formation of quark matter and constrains baryon distributions, inducing statistical repulsion among baryon species. Applying the model to charge-neutral matter composed of neutrons, ${\mathrm{\Lambda }}_0$, and ${\mathrm{\Sigma }}_0$ hyperons, we find that, for typical size of baryons, $d$-quark saturation occurs before hyperons appear, delaying their onset and shifting the threshold density from $\sim 2-3n_{\mathrm{sat}}$ to $\sim 5-6n_{\mathrm{sat}}$ ($n_{\mathrm{sat}}\approx 0.16{\mathrm{fm}}^{-3}$: nuclear saturation density). After hyperons emerge, low-momentum hyperon states remain only sparsely occupied due to the quark saturation. These features mitigate the hyperon puzzle, in which the appearance of hyperons softens neutron star equations of state significantly by increasing energy density with little pressure increase. Our results highlight the key role of quark saturation in dense baryonic matter and provide new insights into the interplay between quark dynamics and hyperon physics in neutron stars.

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• Equations of state of nuclear matter
• Nuclear matter in neutron stars
• QCD in nuclear reactions
• QCD phase transitions
• Quantum chromodynamics
• Hyperons
• Neutron stars & pulsars