feat: add localized home routes

src/pages/Favorites/index.tsx

@@ -1,11 +1,12 @@
 import { Heart } from "lucide-react";
 import { Link } from "react-router-dom";
 import { useI18n } from "../../i18n";
+import { homePathForLang } from "../../languageRoutes";
 import { Reveal } from "../../motion";
 import { useSetPageTitle } from "../../components/PageTitleContext";
 
 export default function Favorites() {
-  const { t } = useI18n();
+  const { lang, t } = useI18n();
   // Show "我的收藏" in the global header, consistent with the other pages.
   useSetPageTitle(t("favorites"));
 
@@ -32,7 +33,7 @@ export default function Favorites() {
       </p>
 
       <Link
-        to="/"
+        to={homePathForLang(lang)}
         className="mt-4 inline-flex h-11 items-center justify-center rounded-full border border-ark-gold/60 bg-ark-gold/10 px-6 text-sm font-medium text-ark-gold transition hover:bg-ark-gold/20 focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-ark-gold/80 focus-visible:ring-offset-2 focus-visible:ring-offset-ark-bg"
       >
         {t("backToHome")}

src/pages/LocalizedHome/index.tsx

@@ -0,0 +1,13 @@
+import { useEffect } from "react";
+import { type Lang, useI18n } from "../../i18n";
+import { Home } from "../Home";
+
+export function LocalizedHomePage({ targetLang }: { targetLang: Lang }) {
+  const { setLang } = useI18n();
+
+  useEffect(() => {
+    setLang(targetLang);
+  }, [setLang, targetLang]);
+
+  return <Home />;
+}