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/plan/plan_test.go

@@ -375,9 +375,9 @@ func TestDraftEmitsPlanReady(t *testing.T) {
 	}
 	for _, r := range rows {
 		p := r.Payload
-		if r.Key != "plan_ready:2026-10-12" || p.Tag != r.Key || p.URL != "/plan" || p.Week != "2026-10-12" ||
+		if r.Key != "plan_ready:2026-10-12" || p.Tag != r.Key || p.URL != "/plan?week=2026-10-12" || p.Week != "2026-10-12" ||
 			p.Title != want.Title || p.Body != "Beef Chili, Pot Roast, Pad Thai + 4 more" {
-			t.Errorf("%s row = %+v, want key plan_ready:2026-10-12, title %q, the drafted dinners and /plan", r.Channel, r, want.Title)
+			t.Errorf("%s row = %+v, want key plan_ready:2026-10-12, title %q, the drafted dinners and /plan?week=2026-10-12", r.Channel, r, want.Title)
 		}
 	}