To further promote rural revitalization strategies and achieve common prosperity, it is necessary to clarify the relationships among public expenditure for agriculture, agricultural green total factor productivity (AGTFP), and the urban–rural income gap (URIG). On the basis of panel data for 30 provincial regions in China from 2012 to 2022, this study constructs a panel vector autoregression (PVAR) model and explores their mutual interaction and influence from both dynamic and static perspectives through the Granger causality test, impulse response analysis, and variance decomposition methods. The research results show that public expenditure on agriculture, AGTFP, and URIG exhibit significant self-reinforcing trends. There is a significant two-way interaction effect between public expenditure on agriculture and URIG, indicating that these factors promote and complement each other. In addition, both improving AGTFP and increasing public expenditure on agriculture can help narrow URIG, but the positive impact of AGTFP exhibits greater magnitude and sustainability. In conclusion, from a long-term perspective, to develop the rural economy and promote rural revitalization, it is necessary not only to increase public expenditure on agriculture continuously, but also to focus on enhancing AGTFP.

As digital education continues to deepen, how teachers’ digital literacy affects students’ well-being has become an important issue with both educational value and public health significance. To move beyond the limitations of traditional variable-centered thinking and to respond to the theoretical demand of viewing digital literacy as a complex system, this study adopts a configurational theoretical perspective and employs fuzzy-set qualitative comparative analysis (fsQCA). Based on data from 540 questionnaire surveys, it systematically explores the multiple concurrent causal mechanisms through which different dimensions of teachers’ digital literacy influence students’ well-being. The findings show that: (1) professional development, digital application, and digital social responsibility are core necessary conditions for enhancing students’ well-being; (2) digital awareness and digital technology knowledge and skills, as auxiliary conditions, form multiple equivalent configurational pathways in combination with the core conditions, indicating that there is no single optimal path to improving students’ well-being; and (3) the multidimensional synergistic effects of teachers’ digital literacy highlight the importance of systematic integration, as improvement in a single dimension alone is insufficient to comprehensively promote students’ well-being. This study not only methodologically demonstrates the applicability of configurational analysis in revealing complex education–health mechanisms, but also extends the theoretical explanation of adolescent well-being as a public health outcome from a systems perspective. It provides evidence-based intervention implications for teacher development in the digital transformation of education, thereby linking the dual goals of improving educational quality and promoting population health at both theoretical and practical levels.