How does community of inquiry matter? Mediating effects and configurational pathways linking project-based learning design to learning engagement

The widespread adoption of generative artificial intelligence (AIGC) has reshaped animation students' skill profiles and the conditions of instructional design in project-based learning (PBL) studios. We examine whether and how perceptions of PBL design are associated with Learning Engagement (LE), treating AIGC-assisted PBL studios as the research context rather than testing generative AI as a model variable. Drawing on Community of Inquiry (CoI) theory, we examine Problem Driven (PD), Project Design (PDe), Project Implementation (PI), and Project Evaluation (PE) as antecedents; Cognitive Presence (CP), Social Presence (SP), and Teaching Presence (TP) as statistical mediators; and LE as the outcome. We analyzed two-wave survey data from 490 upper-year animation students using PLS-SEM and fsQCA. PBL and CoI were measured concurrently at T1, and LE at T2; indirect effects therefore represent indirect statistical associations rather than mediation with a fully established temporal sequence. PD, PDe, and PI showed significant positive direct associations with LE. PE's zero-order and single-predictor associations were positive, but its direct path coefficient became significantly negative after controlling for the other PBL dimensions and CoI mediators. The coefficient was sensitive to model specification, suggesting possible statistical suppression; it should not be interpreted as evidence that evaluation itself inherently inhibits engagement. The three CoI dimensions showed significant statistical mediation associations across all 12 indirect paths. TP and SP had relatively higher point estimates of indirect statistical associations, but differences between indirect effects were not formally tested; no dimension is claimed to be optimal. PE's positive indirect associations through CoI partially offset its negative net direct association without reversing the total association after adjustment. The extent of this offset may depend on the degree to which CoI-related experiences are concurrently reported. fsQCA identified seven high-engagement configurations. No individual PBL dimension was indispensable. CoI dimensions appeared as core or peripheral conditions, although not every configuration included all three. These findings clarify the dual pathways linking evaluation and engagement through indirect statistical associations and configurational conditions, and provide guidance for optimizing PBL under different resource constraints. Conclusions are limited to AIGC-assisted PBL studios and do not establish the instructional effects of generative AI.