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/home/home_test.go

@@ -245,6 +245,7 @@ func TestHomeEmpty(t *testing.T) {
 	h := e.at(t, "2026-10-13 23:59")
 	want := home.Home{
 		DateLabel: "Tuesday, Oct 13",
+		Timezone:  zone,
 		ShoppingList: home.ShoppingStatus{
 			WeekStart: "2026-10-12", Label: "Week 42 · Oct 12 – 18",
 		},
@@ -289,6 +290,32 @@ func TestSideQuestCount(t *testing.T) {
 	}
 }
 
+// Reading Home writes nothing: a batch still pending whose job is gone,
+// which a Deck read would fail, is left as it was, and the read succeeds.
+func TestGetDoesNotWriteBatches(t *testing.T) {
+	t.Parallel()
+	e := newEnv(t)
+	ctx := t.Context()
+	created := "2026-10-13T12:00:00.000Z"
+	batch, err := db.New(e.st.Writer).CreateSuggestionBatch(ctx, db.CreateSuggestionBatchParams{ID: store.NewID(), Trigger: "manual", CreatedAt: created, UpdatedAt: created})
+	if err != nil {
+		t.Fatal(err)
+	}
+	if batch.Status != "pending" {
+		t.Fatalf("new batch status = %q, want pending", batch.Status)
+	}
+	if h := e.at(t, "2026-10-13 12:00"); h.SideQuestCount != 0 {
+		t.Errorf("sideQuestCount = %d, want 0", h.SideQuestCount)
+	}
+	var status, updatedAt string
+	if err := e.st.Reader.QueryRowContext(ctx, `SELECT status, updated_at FROM suggestion_batches WHERE id = ?`, batch.ID).Scan(&status, &updatedAt); err != nil {
+		t.Fatal(err)
+	}
+	if status != "pending" || updatedAt != created {
+		t.Errorf("batch after a Home read = %s at %s, want pending at %s", status, updatedAt, created)
+	}
+}
+
 // The Supply run shown is the upcoming week's when it has one, else the
 // current week's; the weeks are the household's local weeks.
 func TestShoppingStatus(t *testing.T) {