Learned surgical simulators and world models can roll out plausible procedural futures, but they carry no grounded estimate of how often interventional devices actually harm patients. We propose treating population-scale adverse-event surveillance as a distinct belief layer of the surgical digital twin, and we evaluate a federated Bayesian protocol for learning it under formal privacy guarantees. Each site holds per-class Gamma-Poisson posteriors over adverse-event rates and exchanges only Rényi-differentially-private natural-parameter updates. We benchmark on the complete FDA MAUDE cohort for thrombus-retrieval catheters (product code NRY): 8,617 reports, of which 6,491 are classified by transparent keyword rules into five thrombectomy complication classes and partitioned across $K=8$ manufacturer sites. At a matched privacy budget of $(\\varepsilon \\approx 2.09, \δ= 10^{-5})$, the conjugate protocol attains a held-out Poisson score of -5.78 per test event versus -26.58 for FedAvg with differential privacy. The non-private federated model also outperforms centralized pooling (+3.19 vs +2.93), evidence that manufacturer-specific complication profiles are real and that federation preserves them. Because MAUDE lacks procedure denominators, outputs are relative rate orderings rather than absolute risks, and we report all privacy-utility operating points.