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/types.ts

@@ -21,6 +21,7 @@ export interface ProviderConfig {
 	model: string;
 	base_url?: string;
 	enable_tools?: boolean;
+	session_id?: string;
 }
 
 export interface FileEntry {
@@ -52,6 +53,7 @@ export type WsRequest =
 export type WsResponse =
 	| { type: "token"; content: string }
 	| { type: "update"; messages: Message[] }
+	| { type: "session_id"; session_id: string }
 	| { type: "error"; message: string };
 
 // Re-export API client types for convenience