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/context/AuthContext.tsx

@@ -222,6 +222,7 @@ export function useApi(): WorkspaceBoundApi {
 
   return useMemo<WorkspaceBoundApi>(() => ({
    listScripts: (parentPath) => rawApi.listScripts(workspaceId, parentPath),
+   countScripts: () => rawApi.countScripts(workspaceId),
    listResources: (opts) => rawApi.listResources(workspaceId, opts),
    createScript: (input) => rawApi.createScript(workspaceId, input),
     uploadScript: (file, parentPath, visibility) =>

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");

frontend/app/features/platform/state/scriptWorkspaceStore.ts

@@ -91,6 +91,11 @@ type State = {
   // every cache entry that has been loaded in this session.
   loadedScriptPaths: Set<string>;
   loadingScriptPaths: Set<string>;
+  // Workspace-wide active-script total — separate from the lazy-loaded
+  // `scripts` array so dashboards don't underreport. `null` until the
+  // first loadScriptCount() resolves; the count endpoint is cheap.
+  scriptCount: number | null;
+  scriptCountLoading: boolean;
 
   // 只读内容刷新版本号（用于触发已打开标签页的内容刷新）
   readOnlyRefreshVersion: number;
@@ -131,6 +136,9 @@ type State = {
   // Lazy-load scripts directly under `parentPath`. Idempotent — repeated
   // calls for an already-loaded path are no-ops; in-flight calls dedupe.
   loadScripts: (parentPath: string) => Promise<void>;
+  // Fetch the workspace-wide active-script total. Cheap; the dashboard
+  // uses this for its hero count so it doesn't depend on lazy-loaded state.
+  loadScriptCount: () => Promise<void>;
   toggleScriptLock: (script: ScriptItem) => Promise<void>;
   openPublishDialog: (script: ScriptItem) => void;
   submitPublish: (releaseNote: string, visibility: Visibility) => Promise<void>;
@@ -215,6 +223,9 @@ export const useScriptWorkspaceStore = create<State>((set, get) => {
     loadedScriptPaths: new Set<string>(),
     loadingScriptPaths: new Set<string>(),
 
+    scriptCount: null,
+    scriptCountLoading: false,
+
     readOnlyRefreshVersion: 0,
 
     setApiOnline: (online) => set({ apiOnline: online }),
@@ -255,6 +266,8 @@ export const useScriptWorkspaceStore = create<State>((set, get) => {
         loadedChildPaths: new Set<string>(),
         loadedScriptPaths: new Set<string>(),
         loadingScriptPaths: new Set<string>(),
+        scriptCount: null,
+        scriptCountLoading: false,
       });
     },
 
@@ -382,6 +395,22 @@ export const useScriptWorkspaceStore = create<State>((set, get) => {
       }
     },
 
+    loadScriptCount: async () => {
+      const api = requireApi();
+      if (get().scriptCountLoading) return;
+      set({ scriptCountLoading: true });
+      try {
+        const total = await api.countScripts();
+        set({ scriptCount: total });
+      } catch {
+        // Leave previous value in place; the dashboard already tolerates
+        // a stale count by rendering `scriptCount ?? 0`. Don't toast —
+        // the dashboard's other metrics are best-effort.
+      } finally {
+        set({ scriptCountLoading: false });
+      }
+    },
+
     loadChildren: async (parentPath) => {
       const api = requireApi();
       if (get().loadedChildPaths.has(parentPath)) return;

frontend/app/services/api.ts

@@ -296,6 +296,22 @@ export async function listScripts(
   return apiRequest<ScriptItem[]>(`/api/v1/scripts${query}`, {}, workspaceId);
 }
 
+export async function countScripts(
+  workspaceId: string,
+): Promise<number> {
+  // Backend route /api/v1/scripts/count must be declared BEFORE the
+  // /scripts/{script_id} route on the server side. Returns
+  // { data: { total: number } } — the dashboard's single source of
+  // truth for "total active scripts in workspace", independent of the
+  // lazy-loaded scripts[] in the workspace store.
+  const envelope = await apiRequest<{ total: number }>(
+    "/api/v1/scripts/count",
+    {},
+    workspaceId,
+  );
+  return envelope.total;
+}
+
 function initialContent(scriptType: ScriptType): string {
   if (scriptType === "python") {
     return [
@@ -1466,6 +1482,7 @@ export type WorkspaceBoundApi = {
   listScripts: (
     parentPath?: Parameters<typeof listScripts>[1],
   ) => Promise<ScriptItem[]>;
+  countScripts: () => Promise<number>;
   listResources: (
     opts?: Parameters<typeof listResources>[1],
   ) => Promise<ResourceItem[]>;