feat(home): clean shared top bar with live online counter

The homepage duplicated the online count and recent-user avatars (hero plus
community sidebar), and the public pages each kept their own chrome. Put one
AuthTopBar at the top of index, login and register — logo + hotel name plus a
live online indicator and the language/clock/theme controls — and drop the
duplicated hero rows.

src/app/(site)/page.tsx

@@ -10,7 +10,6 @@ import { AnimatedCounter } from "@/components/animated-counter";
 import { AuthTopBar } from "@/components/auth/auth-top-bar";
 import { LoginForm } from "@/components/auth/login-form";
 import Link from "@/components/link";
-import { LiveOnlineCounter } from "@/components/live-online-counter";
 import { Reveal } from "@/components/motion-reveal";
 import { PublicLoadError } from "@/components/public/load-error";
 import { UserAvatarThumbnail } from "@/components/shared/user-avatar-thumbnail";
@@ -402,9 +401,9 @@ async function Home() {
 
 	return (
 		<div className="flex w-full flex-col gap-14 pb-16 pt-2 md:gap-20 md:pb-24">
-			{/* ── Top bar ── */}
+			{/* ── Top bar: logo + live online + language/clock/theme ── */}
 			<div className="mx-auto w-full max-w-7xl">
-				<AuthTopBar hotelName={hotelName} logo={logo} />
+				<AuthTopBar hotelName={hotelName} logo={logo} online={online} />
 			</div>
 			{/* ── Cinematic hero ── */}
 			<Reveal className="-mx-3 sm:-mx-4 md:-mx-6">
@@ -454,46 +453,6 @@ async function Home() {
 						style={{ opacity: 0.5, zIndex: 1 }}
 					/>
 					<div className="relative z-10 mx-auto flex min-h-[540px] w-full max-w-6xl flex-col items-center justify-center px-4 py-24 text-center sm:min-h-[580px] lg:min-h-[640px]">
-						<span
-							className="glass-chip gap-2.5 px-4 py-2"
-							style={{
-								fontWeight: 800,
-								letterSpacing: "0.14em",
-								textTransform: "uppercase",
-							}}
-						>
-							<span className="relative flex h-2 w-2">
-								<span
-									className="absolute inline-flex h-full w-full animate-ping rounded-full opacity-70"
-									style={{ background: "var(--color-primary)" }}
-								/>
-								<span
-									className="relative inline-flex h-2 w-2 rounded-full"
-									style={{ background: "var(--color-primary)" }}
-								/>
-							</span>
-							<span
-								className="text-[10px] font-black sm:text-xs"
-								style={{ color: "var(--color-text-readable)" }}
-							>
-								{tp("onlineNow")}
-							</span>
-							{online === null ? (
-								<span className="text-xs">{te("unavailable")}</span>
-							) : (
-								<span
-									className="text-sm sm:text-base"
-									style={{
-										color:
-											"var(--color-primary-readable, var(--color-primary))",
-										fontWeight: 900,
-									}}
-								>
-									<LiveOnlineCounter initial={online} />
-								</span>
-							)}
-						</span>
-
 						<h1
 							className="mt-7 sm:mt-8"
 							style={{ fontFamily: "var(--font-nunito)" }}
@@ -516,37 +475,6 @@ async function Home() {
 							{tp("welcomeBody")}
 						</p>
 
-						{recentUsers !== null && recentUsers.length > 0 && (
-							<div
-								className="animate-fade-in-up mt-7 inline-flex items-center gap-3 rounded-full border px-3 py-1.5"
-								style={{
-									background: "rgba(255,255,255,0.08)",
-									borderColor: "rgba(255,255,255,0.22)",
-									backdropFilter: "blur(12px)",
-									WebkitBackdropFilter: "blur(12px)",
-									animationDelay: "0.08s",
-								}}
-							>
-								<div className="flex -space-x-2.5">
-									{recentUsers.slice(0, 4).map((u) => (
-										<UserAvatarThumbnail
-											key={u.username}
-											figure={u.look}
-											alt={u.username}
-											options={{ direction: 2 }}
-											className="h-9 w-9 rounded-full ring-2 ring-white/70 shadow-lg"
-										/>
-									))}
-								</div>
-								<span
-									className="pr-1 text-[10px] font-extrabold uppercase tracking-[0.22em]"
-									style={{ color: "rgba(255,255,255,0.75)" }}
-								>
-									{tp("recentUsers")}
-								</span>
-							</div>
-						)}
-
 						<div
 							className="animate-fade-in-up mt-9 flex flex-wrap items-center justify-center gap-3"
 							style={{ animationDelay: "0.2s" }}