fix(context): trigger engine start as fire-and-forget in getProjectContext

Previously, getProjectContext awaited ensureEngine() which could block the
HTTP request handler for several seconds while a project engine initialised
(e.g. for newly-registered projects). This caused curl --max-time timeouts
and empty responses on the first request to a new project.

Change: replace await ensureEngine() with onProjectAccessed() (fire-and-forget).
- First request to an unstarted project uses getOrCreateProjectStore directly
  (fast, reads from SQLite) — no blocking.
- Engine starts in background; subsequent requests use the running engine.
- Eliminates timing-dependent restart workarounds in init scripts.

Fixes: fn settings import followed by immediate API calls returning empty.

packages/dashboard/src/__tests__/routes-system.test.ts

@@ -703,16 +703,17 @@ describe("routes/context project scoping helpers", () => {
     expect(getOrCreateSpy).not.toHaveBeenCalled();
   });
 
-  it("getProjectContext falls back to scoped store when ensureEngine throws", async () => {
+  it("getProjectContext triggers background engine start and falls back to scoped store for first request", async () => {
     const store = createMockStore();
     const fallbackStore = createMockStore();
     const getOrCreateSpy = vi.spyOn(projectStoreResolver, "getOrCreateProjectStore").mockResolvedValueOnce(fallbackStore);
 
     const req = { query: { projectId: "proj-123" }, body: {} } as unknown as express.Request;
+    const onProjectAccessedMock = vi.fn();
     const options = {
       engineManager: {
         getEngine: vi.fn().mockReturnValue(undefined),
-        ensureEngine: vi.fn().mockRejectedValue(new Error("startup failed")),
+        onProjectAccessed: onProjectAccessedMock,
       },
     } as any;
 
@@ -721,7 +722,8 @@ describe("routes/context project scoping helpers", () => {
     expect(context.projectId).toBe("proj-123");
     expect(context.engine).toBeUndefined();
     expect(context.store).toBe(fallbackStore);
-    expect(options.engineManager.ensureEngine).toHaveBeenCalledWith("proj-123");
+    // Engine start is triggered as fire-and-forget — not blocking the request
+    expect(onProjectAccessedMock).toHaveBeenCalledWith("proj-123");
     expect(getOrCreateSpy).toHaveBeenCalledWith("proj-123");
   });
 });

packages/dashboard/src/routes/context.ts

@@ -83,11 +83,11 @@ export async function getProjectContext(
   if (projectId && engineManager) {
     let engine = engineManager.getEngine(projectId);
     if (!engine) {
-      try {
-        engine = await engineManager.ensureEngine(projectId);
-      } catch {
-        // fall through
-      }
+      // Trigger lazy engine start as fire-and-forget so this request is not
+      // blocked while the engine initialises (engine.start() may take several
+      // seconds for a newly-registered project).
+      // The engine will be available for subsequent requests once it starts.
+      engineManager.onProjectAccessed(projectId);
     }
     if (engine) {
       return { store: engine.getTaskStore(), engine, projectId };