Our work highlights the crucial role played by the equation of state (EoS) parameter $w$ within the context of single field inflation with Multiple Sharp Transitions (MSTs) to untangle the current state of the PBH overproduction issue. We examine the situation for a broad interval of EoS parameter that remains most favourable to explain the recent data released by the pulsar timing array (PTA) collaboration. Our analysis yields the interval, $0.2\le w\le 1/3$, to be the most acceptable window from the SIGW interpretation of the PTA signal and where sizeable PBHs abundance, $f_{\mathrm{PBH}}\in (10^{-3},1)$, is observed. We also obtain $w=1/3$, radiation-dominated era, to be the best scenario to explain the early stages of the Universe and address the overproduction problem. Within the range of $1\le c_s\le 1.17$, we construct a regularized-renormalized-resummed scalar power spectrum whose amplitude obeys the perturbativity criterion while being substantial enough to generate EoS dependent scalar induced gravitational waves ($w$-SIGWs) consistent with NANOGrav-15 data. Working for both $c_s=1\mathrm{and}1.17$, we find the $c_s=1.17$ case more favourable for generating large mass PBHs, $M_{\mathrm{PBH}}\sim \mathcal{O}(10^{-6}-10^{-3})M_{\odot }$, as potential dark matter candidates with substantial abundance after constraints coming from microlensing experiments.