feat: add calibration sync system.

backend/routers/calibration.py

@@ -0,0 +1,31 @@
+"""
+Calibration Sync Router
+
+Endpoints for triggering and inspecting the SFM-driven calibration sync.
+The scheduled job runs daily; this router is what the "Sync now" button in
+Settings calls, plus a status endpoint for diagnostics.
+"""
+
+from fastapi import APIRouter
+from typing import Dict, Any
+
+from backend.services.calibration_sync import (
+    sync_all_calibrations,
+    get_calibration_sync_scheduler,
+)
+
+router = APIRouter(prefix="/api/calibration", tags=["calibration"])
+
+
+@router.post("/sync")
+async def trigger_calibration_sync() -> Dict[str, Any]:
+    """Run a full calibration sync now and return the summary."""
+    summary = await sync_all_calibrations()
+    get_calibration_sync_scheduler().last_run = summary
+    return summary
+
+
+@router.get("/sync/status")
+def calibration_sync_status() -> Dict[str, Any]:
+    """Return scheduler status and the most recent run's summary."""
+    return get_calibration_sync_scheduler().status()