feat(scripts): GET /api/v1/scripts/count + DashboardRoute wiring

After #34 the workspace store only holds the root-level scripts plus
whatever subfolders the user has expanded. DashboardRoute's
"全部脚本"/"工作副本" counts derived from scripts.length therefore
underreport the workspace total until the user navigates to /scripts
and expands every folder.

Fix: separate count endpoint + dedicated store field, mounted
independently.

Backend — backend/src/backend/scripts.py
- New endpoint GET /api/v1/scripts/count.
- Route declared BEFORE /api/v1/scripts/{script_id}/... so FastAPI's
  declaration-order matching does not interpret "count" as a script_id.
- Returns { data: { total: number }, meta: {} }; SQL is a single
  COUNT(*) on scripts filtered by workspace_id + status='active'.

Frontend — services/api.ts + context/AuthContext.tsx
- countScripts(workspaceId) client; WorkspaceBoundApi gains the field;
  AuthContext binding forwards workspaceId.

Frontend — state/scriptWorkspaceStore.ts
- scriptCount: number | null, scriptCountLoading: boolean.
- loadScriptCount() action: idempotent (no-op while in-flight), silent
  on failure (dashboard tolerates a stale count).
- Initial state and reset() clear both fields.

Frontend — features/platform/DashboardRoute.tsx
- Subscribes to scriptCount; calls loadScriptCount() on mount.
- Falls back to scripts.length until the count resolves so the
  dashboard never blanks.

Tests — backend/tests/test_count_scripts.py (new)
- 3 unit tests: scalar result handling, NULL coercion, route callable.

Verified: pytest 55 passed (52 + 3 new); pnpm typecheck clean.

frontend/app/features/platform/DashboardRoute.tsx

@@ -1,3 +1,4 @@
+import { useEffect } from "react";
 import { useNavigate } from "react-router";
 
 import { DashboardPage } from "../../components/admin/DashboardPage";
@@ -5,12 +6,21 @@ import { useScriptWorkspaceStore } from "./state/scriptWorkspaceStore";
 
 export default function DashboardRoute() {
   const scripts = useScriptWorkspaceStore((s) => s.scripts);
+  const scriptCount = useScriptWorkspaceStore((s) => s.scriptCount);
+  const loadScriptCount = useScriptWorkspaceStore((s) => s.loadScriptCount);
   const apiOnline = useScriptWorkspaceStore((s) => s.apiOnline);
   const navigate = useNavigate();
 
+  // Independent of the lazy-loaded `scripts` array — the count endpoint
+  // returns the workspace-wide total even when no folders have been
+  // expanded yet (see #34 + #37).
+  useEffect(() => {
+    void loadScriptCount();
+  }, [loadScriptCount]);
+
   return (
     <DashboardPage
-      scriptCount={scripts.length}
+      scriptCount={scriptCount ?? scripts.length}
       online={apiOnline}
       onNavigate={(page) => {
         if (page === "scripts") navigate("/scripts");