We report the design and results of the third autoPET challenge (MICCAI 2024), which benchmarked automated lesion segmentation in whole-body PET/CT under a compositional generalization setting. Training data comprised 1,014 [18F]-FDG PET/CT studies from the University Hospital Tübingen and 597 [18F]/[68Ga]-PSMA PET/CT studies from the LMU University Hospital Munich, constituting the largest publicly available annotated PSMA PET/CT dataset to date. The held-out test set of 200 studies covered four tracer-center combinations, two of which represented unseen compositional pairings. A complementary data-centric award category isolated the contribution of data handling strategies by restricting participants to a fixed baseline model. Seventeen teams submitted 27 algorithms, predominantly nnU-Net-based 3D networks with PET/CT channel concatenation. The top-ranked algorithm achieved a mean DSC of 0.66, FNV of 3.18 mL, and FPV of 2.78 mL across all four test conditions, improving DSC by 8% and reducing the false-negative volume by 5 mL relative to the provided baseline. Ranking was stable across bootstrap resampling and alternative ranking schemes for the top tier. Beyond the benchmark, we provide an in-depth analysis of segmentation performance at the patient and lesion level. Three main conclusions can be drawn: (1) in-domain multitracer PET/CT segmentation is sufficient and probably approaching reader agreement; (2) compositional generalization to unseen tracer-center combinations remains an open problem mainly driven by systematic volume overestimation; (3) heterogeneity and case difficulty drive performance variation substantially more than the choice of algorithm among top-ranked teams.