We present a new cosmological analysis of the small-scale (k ≈ 1-8 h/Mpc) Lyman-α forest 1D flux power spectrum (P1D), using high-resolution quasar spectra from XQ100 and KODIAQ-SQUAD interpreted with the PRIYA simulation based emulator. The Lyα P1D is a unique probe of structure formation on Mpc scales, sensitive to dark matter models and also tracing astrophysical processes such as He II reionization and feedback. PRIYA is the first simulation suite to jointly span cosmological parameters and inhomogeneous He II reionization, enabling a full exploration of the covariance between cosmology and astrophysics at these scales. With this framework, we infer cosmological constraints from the XQ100 and KODIAQ-SQUAD P1D, finding agreement between XQ100 and eBOSS cosmology, while KODIAQ-SQUAD shows a biasedly high matter clustering driven by high-column-density absorber selection. High-resolution P1D data provides tighter constraints on the IGM thermal history and absorber abundance than medium-resolution surveys, offering complementary information to DESI. This complementarity can help break degeneracies between IGM physics and cosmology in future DESI Lyα forest P1D analyses.