feat(27-01): create BottomTabBar component

- Fixed bottom tab bar for mobile (md:hidden) with z-20 stacking
- 4 tabs: Home, Collection, Setups, Search with Lucide icons
- Collection and Setups fire openAuthPrompt for anonymous users
- Search tab calls openCatalogSearch('collection') to open overlay
- Active route highlighting via useMatchRoute
- Framer Motion entry animation (y slide + fade)
- iOS safe area padding with env(safe-area-inset-bottom)

[Rule 1 - Bug] Used 'house' icon instead of 'home': lucide-react has no 'Home' icon (only 'House')

src/client/components/BottomTabBar.tsx

@@ -0,0 +1,95 @@
+import { Link, useMatchRoute } from "@tanstack/react-router";
+import { motion } from "framer-motion";
+import { useAuth } from "../hooks/useAuth";
+import { LucideIcon } from "../lib/iconData";
+import { useUIStore } from "../stores/uiStore";
+
+interface TabItemProps {
+	icon: string;
+	label: string;
+	isActive: boolean;
+}
+
+function TabItemWrapper({
+	icon,
+	label,
+	isActive,
+	children,
+}: TabItemProps & { children?: React.ReactNode }) {
+	const activeClass = "text-gray-900";
+	const inactiveClass = "text-gray-400";
+	const colorClass = isActive ? activeClass : inactiveClass;
+
+	return (
+		<span className={`flex flex-col items-center gap-0.5 py-2 px-4 ${colorClass}`}>
+			<LucideIcon name={icon} size={20} />
+			<span className="text-xs">{label}</span>
+		</span>
+	);
+}
+
+export function BottomTabBar() {
+	const { data: auth } = useAuth();
+	const isAuthenticated = !!auth?.user;
+	const openCatalogSearch = useUIStore((s) => s.openCatalogSearch);
+	const openAuthPrompt = useUIStore((s) => s.openAuthPrompt);
+	const matchRoute = useMatchRoute();
+
+	const isHome = !!matchRoute({ to: "/" });
+	const isCollection = !!matchRoute({ to: "/collection", fuzzy: true });
+	const isSetups = !!matchRoute({ to: "/setups", fuzzy: true });
+
+	return (
+		<motion.div
+			initial={{ y: 20, opacity: 0 }}
+			animate={{ y: 0, opacity: 1 }}
+			transition={{ duration: 0.2, ease: "easeOut" }}
+			className="fixed bottom-0 left-0 right-0 md:hidden z-20 bg-white border-t border-gray-100 pb-[env(safe-area-inset-bottom)]"
+		>
+			<div className="flex justify-around">
+				{/* Home tab — always a Link */}
+				<Link to="/">
+					<TabItemWrapper icon="house" label="Home" isActive={isHome} />
+				</Link>
+
+				{/* Collection tab — Link if authenticated, button if anonymous */}
+				{isAuthenticated ? (
+					<Link to="/collection">
+						<TabItemWrapper
+							icon="package"
+							label="Collection"
+							isActive={isCollection}
+						/>
+					</Link>
+				) : (
+					<button type="button" onClick={openAuthPrompt}>
+						<TabItemWrapper
+							icon="package"
+							label="Collection"
+							isActive={isCollection}
+						/>
+					</button>
+				)}
+
+				{/* Setups tab — Link if authenticated, button if anonymous */}
+				{isAuthenticated ? (
+					<Link to="/setups">
+						<TabItemWrapper icon="layers" label="Setups" isActive={isSetups} />
+					</Link>
+				) : (
+					<button type="button" onClick={openAuthPrompt}>
+						<TabItemWrapper icon="layers" label="Setups" isActive={isSetups} />
+					</button>
+				)}
+
+				{/* Search tab — always a button, opens CatalogSearchOverlay */}
+				<button
+					type="button"
+					onClick={() => openCatalogSearch("collection")}
+				>
+					<TabItemWrapper icon="search" label="Search" isActive={false} />
+				</button>
+			</div>
+		</motion.div>
+	);
+}