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>

internal/server/home_test.go

@@ -35,6 +35,7 @@ func TestGetHome(t *testing.T) {
 		}
 		body, err := json.Marshal(map[string]any{
 			"dateLabel":      now.In(loc).Format("Monday, Jan 2"),
+			"timezone":       loc.String(),
 			"tonight":        nil,
 			"sideQuestCount": 0,
 			"shoppingList":   map[string]any{"weekStart": week.String(), "label": label, "ready": false, "sentToChatAt": nil},