登录页 mode 参数改为服务端直传，消除登录/注册表单切换闪烁

LoginPage 从 searchParams 提取 mode 作为 initialMode prop 传给 LoginClient，
替代客户端 useEffect 从 window.location.search 读取的方式，首次渲染即显示目标表单。

Tested: tsc --noEmit 通过, npm run build 通过

frontend/app/auth/login/page.tsx

@@ -2,7 +2,7 @@ import { LoginClient } from "@/components/auth/LoginClient";
 import { I18nProvider } from "@/hooks/useI18n";
 
 type PageProps = {
-  searchParams?: Promise<{ next?: string }>;
+  searchParams?: Promise<{ next?: string; mode?: string }>;
 };
 
 function normalizeNextPath(input: string | undefined) {
@@ -14,12 +14,18 @@ function normalizeNextPath(input: string | undefined) {
   return raw;
 }
 
+function normalizeMode(input: string | undefined): "login" | "signup" {
+  if (input === "signup") return "signup";
+  return "login";
+}
+
 export default async function LoginPage({ searchParams }: PageProps) {
   const params = (await searchParams) || {};
   const nextPath = normalizeNextPath(params.next);
+  const initialMode = normalizeMode(params.mode);
   return (
     <I18nProvider>
-      <LoginClient nextPath={nextPath} />
+      <LoginClient nextPath={nextPath} initialMode={initialMode} />
     </I18nProvider>
   );
 }

frontend/components/auth/LoginClient.tsx

@@ -26,12 +26,13 @@ type Mode = "login" | "signup";
 
 type LoginClientProps = {
   nextPath: string;
+  initialMode?: Mode;
 };
 
-export function LoginClient({ nextPath }: LoginClientProps) {
+export function LoginClient({ nextPath, initialMode }: LoginClientProps) {
   const router = useRouter();
   const { locale } = useI18n();
-  const [mode, setMode] = useState<Mode>("login");
+  const [mode, setMode] = useState<Mode>(initialMode ?? "login");
   const [email, setEmail] = useState("");
   const [password, setPassword] = useState("");
   const [loading, setLoading] = useState(false);
@@ -40,18 +41,6 @@ export function LoginClient({ nextPath }: LoginClientProps) {
   const [resetSent, setResetSent] = useState(false);
   const [showPassword, setShowPassword] = useState(false);
 
-  useEffect(() => {
-    if (typeof window !== "undefined") {
-      const params = new URLSearchParams(window.location.search);
-      const m = params.get("mode");
-      if (m === "signup") {
-        setMode("signup");
-      } else if (m === "login") {
-        setMode("login");
-      }
-    }
-  }, []);
-
   const supabaseReady = hasSupabasePublicEnv();
   const isLogin = mode === "login";
   const siteOrigin =