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The near-sensor paradigm is widely used in the artificial Intelligence of Things (AIoT) and other emerging applications that require high-performance digital circuits to perform embedded control and signal-processing calculations. This work presents a low-temperature polycrystalline silicon and oxide (LTPO) CMOS-based large-scale integrated circuit (IC) design approach to the flexible sensing and processing system via a unified high-accuracy compact model for LTPO thin-film transistors (TFTs), realizing circuit simulations and reliability evaluations. Grounded in multiple-trapping and releasing theory, the compact model is developed for both low-temperature poly-Si (LTPS) and indium-gallium-zinc oxide (IGZO) TFTs, with an error of much less than $100~\mu \text{V}$ for surface potential. This study delves into the significant aging effect of the positive bias temperature instabilities (PBTI) in IGZO TFTs using calibrated multivariable kinetic equations. The findings suggest that this approach has the potential to enhance the compact integration of sensing and processing systems through the use of advanced LTPO technology ( $\sim 6~\mu \text{m}$ ). Furthermore, LTPO-CMOS-TFTs are used to implement digital circuits, achieving energy efficiency that is $3\times $ higher than the state-of-the-art flexible processors. Compared with widely used pseudo-CMOS logic, complementary logic achieves the improvements of energy consumption and speed by the factors of 122.7 and 3.19, respectively.