Academic burnout, triggered by a combination of external factors and internal psychological characteristics, significantly impacts secondary school students' academic performance and psychological well-being. We use achievement goal orientations, including mastery approach, mastery avoidance, performance approach, and performance avoidance, to identify distinct motivational profiles, in 1137 middle school students. Subsequently, we used regression mixed models and network analysis to examine between-subgroup differences in the relationship between school climate, an external factor, and academic burnout. Latent profile analysis (LPA) revealed three typical patterns of goal pursuit: success-oriented (17.8%), characterized by motivation across various goals; moderated motivation (70%), lacking a salient dominant goal and clear motivational tendency; and unmotivated (12.8%), showing a lack of interest and motivation in learning. Among the success-oriented subgroup, academic burnout was most strongly associated with campus climate. Network comparison results showed stronger links between "student-student support" and "exhaustion," as well as "autonomy" and "efficacy reduction," among students in the success-oriented subgroup compared to those in the unmotivated subgroup. Therefore, educational or counseling programs should be developed, tailored to different goal-seeking models and the specific school climate.