[verified] fix: normalize analytics skill payloads

Normalize /api/analytics/usage responses so older backends that omit
skill analytics do not crash the dashboard.

- add normalizeAnalyticsResponse at the API boundary
- type the page state against the normalized payload
- cover missing and populated skill payloads with tests

web/src/lib/api.analytics.test.ts

@@ -0,0 +1,74 @@
+/// <reference types="node" />
+
+import test from "node:test";
+import assert from "node:assert/strict";
+
+import { normalizeAnalyticsResponse, type AnalyticsResponse } from "./api.ts";
+
+test("normalizeAnalyticsResponse fills in missing skill analytics for older backends", () => {
+  const raw = {
+    daily: [],
+    by_model: [],
+    totals: {
+      total_input: 0,
+      total_output: 0,
+      total_cache_read: 0,
+      total_reasoning: 0,
+      total_estimated_cost: 0,
+      total_actual_cost: 0,
+      total_sessions: 0,
+      total_api_calls: 0,
+    },
+  } as AnalyticsResponse;
+
+  const normalized = normalizeAnalyticsResponse(raw);
+
+  assert.deepEqual(normalized.skills, {
+    summary: {
+      total_skill_loads: 0,
+      total_skill_edits: 0,
+      total_skill_actions: 0,
+      distinct_skills_used: 0,
+    },
+    top_skills: [],
+  });
+});
+
+test("normalizeAnalyticsResponse preserves populated skill analytics", () => {
+  const raw: AnalyticsResponse = {
+    daily: [],
+    by_model: [],
+    totals: {
+      total_input: 0,
+      total_output: 0,
+      total_cache_read: 0,
+      total_reasoning: 0,
+      total_estimated_cost: 0,
+      total_actual_cost: 0,
+      total_sessions: 0,
+      total_api_calls: 0,
+    },
+    skills: {
+      summary: {
+        total_skill_loads: 2,
+        total_skill_edits: 1,
+        total_skill_actions: 3,
+        distinct_skills_used: 2,
+      },
+      top_skills: [
+        {
+          skill: "systematic-debugging",
+          view_count: 2,
+          manage_count: 1,
+          total_count: 3,
+          percentage: 100,
+          last_used_at: 1713900000,
+        },
+      ],
+    },
+  };
+
+  const normalized = normalizeAnalyticsResponse(raw);
+
+  assert.deepEqual(normalized.skills, raw.skills);
+});