feat(matrix): add SvelteKit Matrix client (Phase 1)

Implements a minimal self-hosted Matrix chat client with:
- matrix-js-sdk integration with Svelte 5 runes store
- Password login with homeserver discovery
- Room list (DMs and groups) with unread counts
- Message timeline with typing indicators
- Send messages with Enter key
- Responsive chat UI with Tailwind CSS

Project structure:
- apps/matrix/apps/web: SvelteKit client (port 5180)
- apps/matrix/packages/shared: Shared types

Commands: pnpm dev:matrix:web

https://claude.ai/code/session_01RUrt2qN1D3nVh9HcGpwoby

apps/matrix/packages/shared/src/index.ts

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+// Re-export all types
+export * from './types';

apps/matrix/packages/shared/src/types.ts

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+/**
+ * Shared types for Matrix client
+ */
+
+export type SyncState = 'STOPPED' | 'PREPARED' | 'SYNCING' | 'ERROR' | 'RECONNECTING' | 'CATCHUP';
+
+export interface MatrixCredentials {
+	homeserver: string;
+	accessToken: string;
+	userId: string;
+	deviceId: string;
+}
+
+export type MessageType = 'm.text' | 'm.image' | 'm.file' | 'm.audio' | 'm.video' | 'm.emote' | 'm.notice';
+
+export interface SimpleMessage {
+	id: string;
+	sender: string;
+	senderName: string;
+	body: string;
+	formattedBody?: string;
+	timestamp: number;
+	type: MessageType;
+	isOwn: boolean;
+	replyTo?: string;
+	edited?: boolean;
+}
+
+export interface SimpleRoom {
+	id: string;
+	name: string;
+	topic?: string;
+	avatar?: string;
+	lastMessage?: string;
+	lastMessageSender?: string;
+	lastMessageTime?: number;
+	unreadCount: number;
+	highlightCount: number;
+	isDirect: boolean;
+	isEncrypted: boolean;
+	memberCount: number;
+}