refactor(auth): share the auth landing and extract AuthField

The login and register pages were near-identical after the previous cleanup,
and both forms repeated the same labelled, icon-prefixed input seven times.
Move the data loading and page shell into auth-landing.tsx (loadAuthLanding +
AuthLandingView) and the input markup into a single AuthField, so the pages
become thin compositions and every field shares one focus, icon and aria
implementation. The numbered section headers collapse into AuthSectionHeader.

No behaviour change.

src/app/(site)/register/page.tsx

@@ -1,22 +1,12 @@
-import { desc, eq } from "drizzle-orm";
 import type { Metadata } from "next";
-import { headers } from "next/headers";
 import { redirect } from "next/navigation";
 import { getTranslations } from "next-intl/server";
 import {
-	AuthPageFrame,
-	AuthUsersCards,
-} from "@/components/auth/auth-page-frame";
-import { AuthPromoCard } from "@/components/auth/auth-promo-card";
+	AuthLandingView,
+	loadAuthLanding,
+} from "@/components/auth/auth-landing";
 import { RegisterForm } from "@/components/auth/register-form";
 import { auth } from "@/lib/auth";
-import { cached } from "@/lib/cache";
-
-import { db, User } from "@/lib/db";
-import { resolveHotelName } from "@/lib/hotel-name";
-import { captchaConfig } from "@/lib/services/captcha";
-import { cachedOnlineCount } from "@/lib/services/public-counters";
-import { siteSettings } from "@/lib/services/site-settings";
 
 export async function generateMetadata(): Promise<Metadata> {
 	const t = await getTranslations("pages.register");
@@ -30,77 +20,38 @@ export async function generateMetadata(): Promise<Metadata> {
 }
 
 export default async function RegisterPage() {
-	const tpr = await getTranslations("pages.register");
-	const [hotelName, cfg, logo] = await Promise.all([
-		resolveHotelName(),
-		captchaConfig(),
-		siteSettings.get("cms_logo", ""),
-	]);
-	const nonce = (await headers()).get("x-nonce") ?? undefined;
+	const t = await getTranslations("pages.register");
 
 	// An account already exists in this browser — there is nothing to sign up.
 	const session = await auth();
 	if (session?.user?.id) redirect("/me");
 
-	const [online, recentUsers, latestUsers] = await Promise.all([
-		cachedOnlineCount().catch(() => 0),
-		cached(
-			"auth_online_users",
-			10_000,
-			() =>
-				db
-					.select({ id: User.id, username: User.username, look: User.look })
-					.from(User)
-					.where(eq(User.online, "1"))
-					.limit(8),
-			{ staleMs: 30000 },
-		).catch(() => []),
-		cached(
-			"auth_latest_users",
-			30_000,
-			() =>
-				db
-					.select({ id: User.id, username: User.username, look: User.look })
-					.from(User)
-					.orderBy(desc(User.accountCreated))
-					.limit(8),
-			{ staleMs: 60000 },
-		).catch(() => []),
-	]);
+	const data = await loadAuthLanding();
 
 	return (
-		<AuthPageFrame
-			hotelName={hotelName}
-			logo={logo}
-			title={tpr("title")}
-			subtitle={tpr("subtitle")}
+		<AuthLandingView
+			data={data}
+			copy={{
+				title: t("title"),
+				subtitle: t("subtitle"),
+				promoTitle: (
+					<>
+						{t("title")} —{" "}
+						<span className="gradient-text">{data.hotelName}</span>
+					</>
+				),
+				promoSubtitle: t("subtitle"),
+				usersOnlineLabel: t("usersOnline", { count: data.online }),
+				whoIsOnlineLabel: t("whoIsOnline"),
+				newestCitizensLabel: t("newestCitizens"),
+			}}
 			form={
 				<RegisterForm
-					hotelName={hotelName}
-					captcha={{
-						provider: cfg.provider,
-						siteKey: cfg.siteKey || undefined,
-					}}
-					nonce={nonce}
+					hotelName={data.hotelName}
+					captcha={data.captcha}
+					nonce={data.nonce}
 				/>
 			}
-		>
-			<AuthPromoCard
-				onlineLabel={tpr("usersOnline", { count: online })}
-				title={
-					<>
-						{tpr("title")} — <span className="gradient-text">{hotelName}</span>
-					</>
-				}
-				subtitle={tpr("subtitle")}
-			/>
-
-			<AuthUsersCards
-				recentUsers={recentUsers}
-				latestUsers={latestUsers}
-				recentTitle={tpr("whoIsOnline")}
-				latestTitle={tpr("newestCitizens")}
-			/>
-		</AuthPageFrame>
+		/>
 	);
 }