refactor: store selected week in a cookie, not the URL

The home page no longer reads ?week=YYYY-MM-DD from the URL. Selected week
lives in the tcWeek cookie, set via a server action that revalidates the
home page so the next render reflects it. The URL stays at "/" regardless
of which week the user is viewing.

WeekNav prev/next/today buttons (and the arrow-key bindings) call the
server action directly — no router.refresh dance, no client-side cookie
write. BackToCalendarLink drops its localStorage-based href reconstruction
and just links to "/" since the cookie already remembers the right week
across navigations.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

app/actions/week.ts

@@ -0,0 +1,29 @@
+"use server";
+
+import { cookies } from "next/headers";
+import { revalidatePath } from "next/cache";
+
+const WEEK_COOKIE = "tcWeek";
+const MAX_AGE = 60 * 60 * 24 * 30; // 30 days
+
+/**
+ * Persist the selected week start (YYYY-MM-DD) in a server-readable cookie
+ * and revalidate the home page so the new week renders.
+ */
+export async function setWeek(weekStart: string): Promise<void> {
+  if (!/^\d{4}-\d{2}-\d{2}$/.test(weekStart)) return;
+  const cookieStore = await cookies();
+  cookieStore.set(WEEK_COOKIE, weekStart, {
+    path: "/",
+    maxAge: MAX_AGE,
+    sameSite: "lax",
+  });
+  revalidatePath("/");
+}
+
+/** Clear the saved week — used by the "Today" button to jump back to current. */
+export async function clearWeek(): Promise<void> {
+  const cookieStore = await cookies();
+  cookieStore.delete(WEEK_COOKIE);
+  revalidatePath("/");
+}