feat(mana/web): app picker — autofocused search + alphabetical order

The "App hinzufügen" picker now sorts available apps alphabetically by
their (i18n-resolved) display name and shows an autofocused search input
above the list to filter quickly. Enter selects the first match.
PickerOverlay gains a `subheader` snippet slot so other pickers can
embed their own controls between header and list without having to
re-implement the shell.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

apps/mana/apps/web/src/lib/components/PickerOverlay.svelte

@@ -20,6 +20,9 @@
 		items: TItem[];
 		onClose: () => void;
 		item: Snippet<[TItem, number]>;
+		/** Optional snippet rendered between the header and the list
+		 *  (e.g. a search input). */
+		subheader?: Snippet;
 		/** Optional snippet rendered after the items (e.g. "create custom" button). */
 		footer?: Snippet;
 		emptyLabel?: string;
@@ -32,6 +35,7 @@
 		items,
 		onClose,
 		item,
+		subheader,
 		footer,
 		emptyLabel = 'Keine Einträge',
 		width = '320px',
@@ -45,6 +49,11 @@
 			<X size={16} />
 		</button>
 	</div>
+	{#if subheader}
+		<div class="picker-subheader">
+			{@render subheader()}
+		</div>
+	{/if}
 	<div class="picker-list">
 		{#each items as entry, i}
 			{#if i > 0}<div class="divider"></div>{/if}
@@ -116,6 +125,11 @@
 		color: hsl(var(--color-foreground));
 	}
 
+	.picker-subheader {
+		padding: 0 1rem 0.5rem;
+		flex-shrink: 0;
+	}
+
 	.picker-list {
 		flex: 1;
 		overflow-y: auto;

apps/mana/apps/web/src/lib/components/workbench/AppPagePicker.svelte

@@ -3,6 +3,8 @@
 -->
 <script lang="ts">
 	import { _ } from 'svelte-i18n';
+	import { tick } from 'svelte';
+	import { MagnifyingGlass } from '@mana/shared-icons';
 	import PickerOverlay from '$lib/components/PickerOverlay.svelte';
 	import { getAccessibleApps } from '$lib/app-registry';
 
@@ -23,12 +25,35 @@
 
 	let { onSelect, onClose, activeAppIds = [], userTier = null }: Props = $props();
 
+	let query = $state('');
+	let searchInput = $state<HTMLInputElement | null>(null);
+
 	// Filter twice: tier-gate first (so guests + public users don't see
 	// founder/alpha/beta apps at all), then drop apps that are already
-	// open in the current scene.
+	// open in the current scene. Sort alphabetically by the displayed
+	// (i18n-resolved) name, then apply the search query.
 	let availableApps = $derived(
-		getAccessibleApps(userTier).filter((app) => !activeAppIds.includes(app.id))
+		getAccessibleApps(userTier)
+			.filter((app) => !activeAppIds.includes(app.id))
+			.map((app) => ({ app, displayName: appName(app.id, app.name) }))
+			.sort((a, b) => a.displayName.localeCompare(b.displayName, 'de'))
+			.filter(({ displayName }) =>
+				query.trim() === '' ? true : displayName.toLowerCase().includes(query.trim().toLowerCase())
+			)
+			.map(({ app }) => app)
 	);
+
+	// Auto-focus the search input when the picker opens.
+	$effect(() => {
+		tick().then(() => searchInput?.focus());
+	});
+
+	function handleSearchKeydown(e: KeyboardEvent) {
+		if (e.key === 'Enter' && availableApps.length > 0) {
+			e.preventDefault();
+			onSelect(availableApps[0].id);
+		}
+	}
 </script>
 
 <PickerOverlay
@@ -36,8 +61,21 @@
 	items={availableApps}
 	{onClose}
 	width="300px"
-	emptyLabel="Alle Apps sind bereits geöffnet"
+	emptyLabel={query.trim() === '' ? 'Alle Apps sind bereits geöffnet' : 'Keine Treffer'}
 >
+	{#snippet subheader()}
+		<div class="search-wrap">
+			<MagnifyingGlass size={14} />
+			<input
+				bind:this={searchInput}
+				bind:value={query}
+				type="text"
+				placeholder="Suchen…"
+				class="search-input"
+				onkeydown={handleSearchKeydown}
+			/>
+		</div>
+	{/snippet}
 	{#snippet item(app)}
 		<button class="picker-option" onclick={() => onSelect(app.id)}>
 			<div class="app-dot" style="background-color: {app.color}"></div>
@@ -47,6 +85,32 @@
 </PickerOverlay>
 
 <style>
+	.search-wrap {
+		display: flex;
+		align-items: center;
+		gap: 0.375rem;
+		padding: 0.375rem 0.625rem;
+		border-radius: 0.375rem;
+		background: hsl(var(--color-muted) / 0.6);
+		color: hsl(var(--color-muted-foreground));
+		transition: background 0.15s;
+	}
+	.search-wrap:focus-within {
+		background: hsl(var(--color-muted));
+	}
+	.search-input {
+		flex: 1;
+		min-width: 0;
+		border: none;
+		outline: none;
+		background: transparent;
+		font-size: 0.8125rem;
+		color: hsl(var(--color-foreground));
+	}
+	.search-input::placeholder {
+		color: hsl(var(--color-muted-foreground));
+	}
+
 	:global(.picker .app-dot) {
 		width: 10px;
 		height: 10px;