refactor(chronik): replace inline filter switch with filterFeed()

Wire the extracted filterFeed function into the displayFeed derived,
removing 20 lines of inline switch logic from +page.svelte.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

frontend/src/routes/chronik/+page.svelte

@@ -11,6 +11,7 @@ import ChronikEmptyState from '$lib/components/chronik/ChronikEmptyState.svelte'
 import ChronikErrorCard from '$lib/components/chronik/ChronikErrorCard.svelte';
 import type { components } from '$lib/generated/api';
 import type { FilterValue } from './+page.server';
+import { filterFeed } from './feedFilters';
 
 type ActivityFeedItemDTO = components['schemas']['ActivityFeedItemDTO'];
 
@@ -92,28 +93,7 @@ async function onMarkAllRead() {
 	await notificationStore.markAllRead();
 }
 
-const displayFeed = $derived<ActivityFeedItemDTO[]>(
+const displayFeed = $derived(filterFeed(data.activityFeed, activeFilter));
-	(() => {
-		const merged = data.activityFeed;
-		switch (activeFilter) {
-			case 'alle':
-				return merged;
-			case 'fuer-dich':
-				return merged.filter((i) => i.kind === 'MENTION_CREATED' || i.youMentioned);
-			case 'hochgeladen':
-				return merged.filter((i) => i.kind === 'FILE_UPLOADED');
-			case 'transkription':
-				return merged.filter(
-					(i) =>
-						i.kind === 'TEXT_SAVED' ||
-						i.kind === 'BLOCK_REVIEWED' ||
-						i.kind === 'ANNOTATION_CREATED'
-				);
-			case 'kommentare':
-				return merged.filter((i) => i.kind === 'COMMENT_ADDED' || i.kind === 'MENTION_CREATED');
-		}
-	})()
-);
 
 const isEmpty = $derived(displayFeed.length === 0);
 const emptyVariant = $derived<'first-run' | 'filter-empty' | 'inbox-zero'>(