Deciphering the Physical Origin of GRB 240825A: A Long GRB Lacking a Bright Supernova

We present a comprehensive multiwavelength analysis of GRB 240825A, a bright gamma-ray burst (GRB) detected by Fermi and Swift, with a prompt duration ($T_{\rm 90}$ ~ 4 sec in 50-300 keV) near the boundary separating short and long GRBs, prompting a detailed investigation into its classification and progenitor. Using classical prompt metrics (duration, minimum variability timescale (MVT), lag, and spectral hardness) and modern classification techniques (machine-learning (ML) based t-SNE, support vector machine, energy-hardness-duration, and $\epsilon \equiv E_{\gamma,\mathrm{iso},52} / E_{p,z,2}^{5/3}$), we find GRB 240825A exhibits hybrid characteristics. The short MVT (13.830 $\pm$ 1.574 ms), rest-frame duration, and ML-based classification indicate a merger-like or ambiguous nature, while its energetics and position on the Amati relation favor a collapsar origin. We conducted deep optical and NIR photometric and spectroscopic late-time search for an associated supernova (SN)/kilonova (KN) and the host galaxy using 10.4 m GTC and 8.4 m binocular LBT telescopes. No bright SN (like SN 1998bw) is detected down to stringent limits (e.g., $m_r>26.1$ mag at 17.59 days), despite a redshift of $z$ = 0.659 measured from GTC spectroscopy. Host galaxy SED modeling with Prospector indicates a massive, dusty, and star-forming galaxy-typical of collapsar GRB hosts, though with low sSFR and large offset. We compare these findings with hybrid events like GRB 211211A, GRB 230307A, GRB 200826A, including SNe-GRBs, and conclude that GRB 240825A likely originated from a massive star collapse, with the associated supernova obscured by a dusty host environment or low luminosity SN with absolute magnitude M$_{V}$ fainter than -18.0. This study emphasizes the need for multiwavelength follow-up and a multi-layered classification to determine GRB progenitors.