refactor(chat): extract XState actors into chat-machine.actors.ts

- Split chat state machine actors (chatInit, sendMessageHttp, loadMoreHistory, chatWebSocket) into a dedicated module
- Add comprehensive console logging across the chat state machine for full trace debugging
- Comment out margin on text bubble CSS for layout adjustment
- Add debug logging to chat input bar send handler
- Clean up redundant comments in auth-screen component

src/app/chat/components/chat-input-bar.tsx

@@ -42,6 +42,13 @@ export function ChatInputBar({ disabled = false }: ChatInputBarProps) {
 
   const handleSend = () => {
     if (!hasContent) return;
+    console.log("[chat-input-bar] handleSend", {
+      contentLength: input.length,
+      contentPreview: input.slice(0, 50),
+      hasContent,
+      disabled,
+      isFocused,
+    });
     dispatch({ type: "ChatSendMessage", content: input });
     setInput("");
     textareaRef.current?.focus();