Accept story 39: Persistent Claude Code Sessions in Web UI

Use --resume <session_id> with claude -p so the web UI claude-code-pty
provider maintains full conversation context across messages, identical
to a long-running terminal Claude Code session.

Changes:
- Capture session_id from claude -p stream-json system event
- Pass --resume on subsequent messages in same chat session
- Thread session_id through ProviderConfig, ChatResult, WsResponse
- Frontend stores sessionId per chat, clears on New Session
- Unset CLAUDECODE env to allow nested spawning from server
- Wait for clean process exit to ensure transcript flush to disk

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

frontend/src/components/Chat.tsx

@@ -81,6 +81,7 @@ export function Chat({ projectPath, onCloseProject }: ChatProps) {
 	const [lastUpcomingRefresh, setLastUpcomingRefresh] = useState<Date | null>(
 		null,
 	);
+	const [claudeSessionId, setClaudeSessionId] = useState<string | null>(null);
 
 	const storyId = "26_establish_tdd_workflow_and_gates";
 	const gateStatusColor = isGateLoading
@@ -500,6 +501,9 @@ export function Chat({ projectPath, onCloseProject }: ChatProps) {
 					setLoading(false);
 				}
 			},
+			onSessionId: (sessionId) => {
+				setClaudeSessionId(sessionId);
+			},
 			onError: (message) => {
 				console.error("WebSocket error:", message);
 				setLoading(false);
@@ -611,6 +615,9 @@ export function Chat({ projectPath, onCloseProject }: ChatProps) {
 				model,
 				base_url: "http://localhost:11434",
 				enable_tools: enableTools,
+				...(isClaudeCode && claudeSessionId
+					? { session_id: claudeSessionId }
+					: {}),
 			};
 
 			wsRef.current?.sendChat(newHistory, config);
@@ -663,6 +670,7 @@ export function Chat({ projectPath, onCloseProject }: ChatProps) {
 			setMessages([]);
 			setStreamingContent("");
 			setLoading(false);
+			setClaudeSessionId(null);
 		}
 	};