Assessing the Impacts of New Quality Productivity on Sustainable Agriculture: Structural Mechanisms and Optimization Strategies—Empirical Evidence from China

New quality productivity (N) in China is examined as a key driver for enhancing innovation and promoting sustainable development, with a focus on its structural framework in agriculture across three primary dimensions: New Quality Agricultural Laborers (NQL), New Quality Agricultural Labor Inputs (NQLI), and New Quality Agricultural Production Inputs (NQPI). This study aims to explore the relationship between new quality productivity and sustainable agriculture in China, analyzing its impact mechanisms and optimization strategies using data from 30 provincial-level regions between 2012 and 2021. Initially, Partial Least Squares Structural Equation Modeling (PLS-SEM) is employed to identify the specific structural relationships influencing NQP. The Outer Loadings TOPSIS (OL-TOPSIS) method quantifies the contributions of each construct in NQP research across China’s agricultural functional zones. The combined IPMA (cIPMA) model is developed to analyze the necessary conditions, thereby formulating specific optimization strategies. The results indicate that, within the structural framework, the overall NQP construct indicators have a significant impact on promoting sustainable agricultural development. Furthermore, locational analysis reveals that each region exhibits a trend of stability and continuous optimization. In the necessity analysis, both NQL (0.378) and NQLI (0.329) meet the required conditions, and NQPI (0.143) does not satisfy the necessity conditions, necessitating prioritized actions.