feat(chat): add app switcher to PillNavigation

- Import getPillAppItems from shared-branding
- Enable showAppSwitcher with all Mana apps
- Current app (chat) is marked in dropdown

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

apps/chat/apps/web/src/routes/(protected)/+layout.svelte

@@ -11,8 +11,12 @@
 	} from '$lib/stores/navigation';
 	import { PillNavigation } from '@manacore/shared-ui';
 	import type { PillNavItem, PillDropdownItem } from '@manacore/shared-ui';
+	import { getPillAppItems } from '@manacore/shared-branding';
 	import type { LayoutData } from './$types';
 
+	// App switcher items
+	const appItems = getPillAppItems('chat');
+
 	let { children, data }: { children: any; data: LayoutData } = $props();
 
 	let isChecking = $state(true);
@@ -177,6 +181,8 @@
 			showLogout={true}
 			onLogout={handleLogout}
 			primaryColor="#3b82f6"
+			showAppSwitcher={true}
+			{appItems}
 		/>
 
 		<!-- Main Content with dynamic padding based on nav mode -->