feat(ui): add app shell, router, and base path handling

Base path comes from BUN_PUBLIC_BASE_PATH so the same bundle serves both
a root Docker deploy and a GitHub Pages subpath.

Deviation from the task-16 brief: does not install @happy-dom/global-registrator,
does not create test/setup.ts, and does not add a [test] preload to bunfig.toml.
A global DOM preload would make src/domain/smoke.test.ts's "importable without a
DOM" assertion vacuously true, silently retiring the check that guards the
domain-layer-stays-pure invariant. Nothing in this task needs a DOM: basePath.test.ts
is pure string logic, and the shell render test was intentionally omitted by the
brief itself. A later task will register happy-dom per-file where a DOM is
genuinely required.

src/ui/App.tsx

@@ -0,0 +1,52 @@
+import { BrowserRouter, Navigate, Route, Routes, NavLink } from "react-router";
+import { ROUTER_BASENAME } from "./basePath.ts";
+import { currentMonth } from "../store/index.ts";
+import { MonthRoute } from "./routes/MonthRoute.tsx";
+import { YearRoute } from "./routes/YearRoute.tsx";
+import { PostMonthRoute } from "./routes/PostMonthRoute.tsx";
+import { PostYearRoute } from "./routes/PostYearRoute.tsx";
+import { SummaryRoute } from "./routes/SummaryRoute.tsx";
+import { SettingsRoute } from "./routes/SettingsRoute.tsx";
+
+export function AppRoutes() {
+  const year = currentMonth.slice(0, 4);
+  return (
+    <div className="min-h-screen bg-background text-foreground">
+      <nav className="flex gap-4 border-b px-6 py-3 text-sm">
+        <NavLink to={`/month/${currentMonth}`} className="hover:underline">
+          Month
+        </NavLink>
+        <NavLink to={`/year/${year}`} className="hover:underline">
+          Year
+        </NavLink>
+        <NavLink to="/summary" className="hover:underline">
+          Summary
+        </NavLink>
+        <NavLink to="/settings" className="ml-auto hover:underline">
+          Settings
+        </NavLink>
+      </nav>
+      <main className="p-6">
+        <Routes>
+          <Route path="/month/:monthId" element={<MonthRoute />} />
+          <Route path="/year/:year" element={<YearRoute />} />
+          <Route path="/post/:postId/month/:monthId" element={<PostMonthRoute />} />
+          <Route path="/post/:postId/year/:year" element={<PostYearRoute />} />
+          <Route path="/summary" element={<SummaryRoute />} />
+          <Route path="/settings" element={<SettingsRoute />} />
+          <Route path="*" element={<Navigate to={`/month/${currentMonth}`} replace />} />
+        </Routes>
+      </main>
+    </div>
+  );
+}
+
+export function App() {
+  return (
+    <BrowserRouter basename={ROUTER_BASENAME}>
+      <AppRoutes />
+    </BrowserRouter>
+  );
+}
+
+export default App;