Project-based learning (PBL) plays a critical role in fostering interdisciplinary integration within science, technology, engineering, and mathematics (STEM) education. However, its complexity often hinders students' ability to apply knowledge and solve problems, particularly in environments that lack psychological and cognitive support. This study aims to address these challenges by constructing a STEM education model centered on PBL and examining the interactions among STEM psychological capital (SPC), problem-solving skills (PS), STEM cognition (SC), and STEM project-based learning performance (SP). In total, 230 seventh-grade students participated in a STEM project-based activity themed "Internet of Things (IoT) Smart Energy-Saving House." Data were collected through questionnaires and performance assessments. Partial least squares structural equation modeling (PLS-SEM) was used to analyze the interactions. By validating the interplay among psychological capital, cognition, and problem-solving abilities in STEM-PBL contexts, this study identifies the critical role of SPC, PS, and SC in enhancing students' SP outcomes and underscores the necessity of integrating psychological support and cognitive development into STEM curricula. Furthermore, the findings provide a novel framework for bridging the gap between theoretical knowledge and practical application, offering valuable insights for future research and educational design.