Background: Respiratory diseases are a leading cause of childhood morbidity and mortality, yet lung auscultation remains subjective and limited by inter-listener variability, particularly in pediatric populations. Existing AI approaches are further constrained by small datasets and single-task designs. We developed PulmoVec, a multi-task framework built on the Health Acoustic Representations (HeAR) foundation model for classification of pediatric respiratory sounds. Methods: In this retrospective analysis of the SPRSound database, 24,808 event-level annotated segments from 1,652 pediatric patients were analyzed. Three task-specific classifiers were trained for screening, sound-pattern recognition, and disease-group prediction. Their out-of-fold probability outputs were combined with demographic metadata in a LightGBM stacking meta-model, and event-level predictions were aggregated to the patient level using ensemble voting. Results: At the event level, the screening model achieved an ROC-AUC of 0.96 (95% CI, 0.95-0.97), the sound-pattern recognition model a macro ROC-AUC of 0.96 (95% CI, 0.96-0.97), and the disease-group prediction model a macro ROC-AUC of 0.94 (95% CI, 0.93-0.94). At the patient level, disease-group classification yielded an accuracy of 0.74 (95% CI, 0.71-0.77), a weighted F1-score of 0.73, and a macro ROC-AUC of 0.91 (95% CI, 0.90-0.93). Stacking improved performance across all tasks compared with base models alone. Conclusions: PulmoVec links event-level acoustic phenotyping with patient-level clinical classification, supporting the potential of foundation-model-based digital auscultation in pediatric respiratory medicine. Multi-center external validation across devices and real-world conditions remains essential.