This Letter presents an analysis of the infrared (∼3─28 μm) spectra extracted from the nuclear (r < 150 pc) regions of four low-luminosity active galactic nuclei (AGN), observed by JWST NIRSpec/integral field unit and MIRI/Medium Resolution Spectroscopy as an extension of the Galaxy Activity, Torus, and Outflow Survey. We find that, compared to higher-luminosity AGN, these low-luminosity AGN exhibit distinct properties in their emission of ionized gas, polycyclic aromatic hydrocarbons (PAHs), and molecular hydrogen (H2). Specifically, the low-luminosity AGN exhibit relatively weak high ionization potential lines (e.g., [Ne V] and [O IV]), and the line ratios suggest that fast radiative shocks (with vs of ∼100s km s−1) are the primary excitation source of ionized gas therein. Under the low-excitation conditions of their nuclear regions, these low-luminosity AGN generally exhibit a higher fraction of PAHs with large size (NC ≳ 200), reflecting the preferential destruction of smaller PAH molecules by AGN feedback. Furthermore, the H2 transitions in these low-luminosity AGN are not fully thermalized, with slow, plausibly jet-driven molecular shocks (with vs ≤ 10 km s−1) likely being the extra excitation source. Taken together with results from the literature, these findings indicate that feedback operates in both low- and high-luminosity AGN, although its impact varies with AGN luminosity. In particular, systematic variations in PAH band ratios are found across AGN, demonstrating the differing influence of feedback in AGN of varying luminosities and highlighting the potential of PAH band ratios as diagnostics for distinguishing kinetic- and radiative-mode AGN feedback.