Fix Home dashboard integration findings (Feature 21)

- F21-01: plan_ready and list_ready links carry their week
  (/plan?week=, /plan/shopping?week=), and the Plan opens on ?week=
  and keeps it on the week shown, so an older update opens its week.
- F21-02: a failed refresh of the Rotation check shows its ErrorBanner
  beside the cached pending card instead of replacing it.
- F21-03: Home carries the household's timezone and is read again at
  its next local midnight.
- F21-04: Home counts pending Side quests through a read-only query
  (suggest.PendingCount), so reading Home never writes batches.

Task: ac3dddf0-a05f-4e43-a5ad-3105fe6bdd95

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

web/src/home/api.test.ts

@@ -1,5 +1,6 @@
 import { describe, expect, it } from 'vitest'
-import { parseUpdates } from './api.ts'
+import { HOME } from '../test/ApiProviders.tsx'
+import { parseHome, parseUpdates } from './api.ts'
 
 const origin = 'https://mealquest.example'
 const where = 'GET /api/v1/updates'
@@ -37,3 +38,15 @@ describe('parseUpdates', () => {
     )
   })
 })
+
+describe('parseHome', () => {
+  it("keeps the household's zone, and refuses one that is not an IANA zone", () => {
+    expect(parseHome('GET /api/v1/home', HOME).timezone).toBe('America/New_York')
+    expect(() => parseHome('GET /api/v1/home', { ...HOME, timezone: 'Mars/Olympus' })).toThrow(
+      'GET /api/v1/home: timezone "Mars/Olympus" is not an IANA zone',
+    )
+    expect(() => parseHome('GET /api/v1/home', { ...HOME, timezone: undefined })).toThrow(
+      'GET /api/v1/home: timezone undefined is not an IANA zone',
+    )
+  })
+})