feat(v0.3): H2 server — Claude Code hooks → live status side-channel

- types: ClaudeStatus + ServerMessage 'status'; Session.claudeStatus;
  SessionManager.handleHookEvent
- session: inject WEBTERM_SESSION + WEBTERM_HOOK_URL into the spawned shell env
  so hooks know which tab they belong to
- http/hook.ts: pure event→status mapper (PreToolUse→working, PermissionRequest/
  Notification:permission_prompt→waiting, Stop/idle_prompt→idle); 6 unit tests
- server: POST /hook (loopback-only, express.json 64kb) → manager pushes 'status'
- fix: closeIdleConnections() on shutdown so an idle hook keep-alive socket
  doesn't hang close()/SIGTERM
- integration ⑦ (real PTY): attach → POST /hook → ws receives status. 205 tests green.

src/types.ts

@@ -44,12 +44,17 @@ export type ClientMessage =
   | { type: 'input'; data: string }
   | { type: 'resize'; cols: number; rows: number };
 
+/** Claude Code activity, derived from hooks (H2). 'unknown' = no hook signal yet. */
+export type ClaudeStatus = 'working' | 'waiting' | 'idle' | 'unknown';
+
 /** server → client. exit.code = shell code; -1 when spawn never succeeded (M4).
- *  exit.reason optional normally, REQUIRED on spawn failure / abnormal exit. */
+ *  exit.reason optional normally, REQUIRED on spawn failure / abnormal exit.
+ *  status (H2) = Claude Code activity pushed from a hook side-channel. */
 export type ServerMessage =
   | { type: 'attached'; sessionId: string }
   | { type: 'output'; data: string }
-  | { type: 'exit'; code: number; reason?: string };
+  | { type: 'exit'; code: number; reason?: string }
+  | { type: 'status'; status: ClaudeStatus; detail?: string };
 
 /** parseClientMessage result — never throws; errors flow here (§5.3). */
 export type ParseResult =
@@ -139,6 +144,8 @@ export interface Session {
    *  and attach replays the buffer then re-sends `exit` (L1). */
   exitedAt: number | null;
   exitCode: number | null;
+  /** Claude Code activity from hooks (H2); updated by manager.handleHookEvent. */
+  claudeStatus: ClaudeStatus;
   readonly pty: IPty;
 }
 
@@ -156,6 +163,8 @@ export interface Session {
 export interface SessionManager {
   handleAttach(ws: WebSocketLike, sessionId: string | null, dims: Dims, now: number): Session;
   get(id: string): Session | undefined;
+  /** Set a session's Claude status (from a hook) and push it to the attached ws (H2). */
+  handleHookEvent(sessionId: string, status: ClaudeStatus, detail?: string): void;
   /** reclaim when now - max(detachedAt, lastOutputAt) > idleTtlMs (M3). Returns count. */
   reapIdle(now: number): number;
   shutdown(): void;