bug: Potential main-thread deadlock in EmbeddedChatApi.ts when typingHandlerLock remains set

Bug Description

When running EmbeddedChat and receiving typing status notifications over the DDP WebSocket connection, the browser tab completely freezes and becomes unresponsive (causing a white screen or canvas freeze in Storybook / React applications).

Root Cause Analysis

Inside packages/api/src/EmbeddedChatApi.ts, the function handleTypingEvent contains a synchronous busy-wait loop:

// packages/api/src/EmbeddedChatApi.ts (Line 456)
setTimeout(() => {
  typingHandlerLock = 0;
}, 2000);

while (typingHandlerLock) {} // <--- Critical Bug
typingHandlerLock = 1;

Start in packages/api/src/EmbeddedChatApi.ts at handleTypingEvent and inspect how typing notifications arrive over the DDP WebSocket connection. Reproduce the freeze while receiving typing status updates, then verify that the browser remains responsive and typing events continue to be handled without the lock blocking the main thread.