Uniform Forward-Modeling Analysis of Ultracool Dwarfs. IV. Benchmarking the Sonora Diamondback and Saumon & Marley (2008) Atmospheric Models Across Late-M, L, and T types with Low-Resolution 0.8-2.5 $μ$m Spectroscopy

(Abridged) We present a systematic assessment of two major cloudy atmospheric model grids -- SM08 (Saumon & Marley 2008) and Sonora Diamondback -- when applied to low-resolution near-infrared (0.8-2.5 $μ$m) spectroscopy. Our analysis focuses on a uniform sample of 142 age-benchmark brown dwarfs and planetary-mass objects spanning late-M, L, and T spectral types, with independently determined ages from 10 Myr to 10 Gyr. We perform forward-model spectral fitting for all benchmarks' IRTF/SpeX spectra ($R\sim$80-250) using both SM08 and Sonora Diamondback atmospheric models to infer effective temperatures, surface gravities, metallicities, radii, and cloud sedimentation efficiencies. The two model grids yield broadly consistent results. Among L4-L9 dwarfs, we identify a statistically significant, population-level age dependence of the cloud parameter $f_{\rm sed}$, with young benchmarks ($