feat(FN-1010): add mission start endpoint and UI button

- Add POST /api/missions/:missionId/start backend endpoint to start planning missions
- Add startMission() frontend API function in dashboard api.ts
- Add Start button in MissionManager component for planning missions
- Add integration tests for the startMission endpoint covering success, error, and edge cases

packages/dashboard/app/api.ts

@@ -2654,6 +2654,13 @@ export function stopMission(missionId: string, projectId?: string): Promise<Miss
   });
 }
 
+/** Start a planning mission: sets status to "active" and activates the first pending slice */
+export function startMission(missionId: string, projectId?: string): Promise<MissionWithHierarchy> {
+  return api<MissionWithHierarchy>(withProjectId(`/missions/${encodeURIComponent(missionId)}/start`, projectId), {
+    method: "POST",
+  });
+}
+
 // ── Mission Autopilot API ────────────────────────────────────────────────
 
 /** Fetch autopilot status for a mission */

packages/dashboard/app/components/MissionManager.tsx

@@ -61,6 +61,7 @@ import {
   pauseMission,
   resumeMission,
   stopMission,
+  startMission,
   fetchMissionAutopilotStatus,
   updateMissionAutopilot,
   startMissionAutopilot,
@@ -686,6 +687,18 @@ export function MissionManager({ isOpen, onClose, addToast, projectId, onSelectT
     }
   }, [addToast, loadMissionDetail, loadMissions, projectId]);
 
+  // Start a planning mission — set status to "active" and activate first slice
+  const handleStartMission = useCallback(async (missionId: string) => {
+    try {
+      await startMission(missionId, projectId);
+      addToast("Mission started — first slice activated", "success");
+      await loadMissionDetail(missionId);
+      loadMissions();
+    } catch (err: any) {
+      addToast(err.message || "Failed to start mission", "error");
+    }
+  }, [addToast, loadMissionDetail, loadMissions, projectId]);
+
   // ── Autopilot handlers ──
 
   const loadAutopilotStatus = useCallback(async (missionId: string) => {
@@ -980,6 +993,16 @@ export function MissionManager({ isOpen, onClose, addToast, projectId, onSelectT
                       <RefreshCw size={14} />
                     </button>
                   )}
+                  {selectedMission.status === "planning" && (
+                    <button
+                      className="mission-icon-btn mission-icon-btn--success"
+                      onClick={() => handleStartMission(selectedMission.id)}
+                      title="Start mission"
+                      aria-label="Start mission"
+                    >
+                      <Play size={14} />
+                    </button>
+                  )}
                   <button
                     className="mission-icon-btn"
                     onClick={() => handleEditMission(selectedMission)}
@@ -1597,6 +1620,15 @@ export function MissionManager({ isOpen, onClose, addToast, projectId, onSelectT
                         <RefreshCw size={14} />
                       </button>
                     )}
+                    {m.status === "planning" && (
+                      <button
+                        className="mission-icon-btn mission-icon-btn--success"
+                        onClick={() => handleStartMission(m.id)}
+                        title="Start mission"
+                      >
+                        <Play size={14} />
+                      </button>
+                    )}
                     <button
                       className="mission-icon-btn"
                       onClick={() => handleEditMission(mission)}