They use backend configurable at environment variable ZED_PREDICT_EDITS_URL https://github.com/zed-industries/zed/blob/2f734cbd5e2452647... , but I don't know if the /predict_edits/v2 endpoint is something some projects provide or not.
At least the model is available and interacting with it seems simple, so it's probably quite realistic to have an open/locally runnable version of it. The model isn't very big.