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/session/manager.ts

@@ -22,7 +22,14 @@
  * Coding style: immutable-update preference, no console.log, errors explicit.
  */
 
-import type { Config, Dims, Session, SessionManager, WebSocketLike } from '../types.js';
+import type {
+  ClaudeStatus,
+  Config,
+  Dims,
+  Session,
+  SessionManager,
+  WebSocketLike,
+} from '../types.js';
 import { WS_OPEN } from '../types.js';
 import { serialize } from '../protocol.js';
 import { createSession, attachWs, kill } from './session.js';
@@ -119,6 +126,20 @@ export function createSessionManager(cfg: Config): SessionManager {
     return sessions.get(id);
   }
 
+  /**
+   * H2: a Claude Code hook reported activity for `sessionId`. Record it and push
+   * a `status` frame to the attached ws (no-op if the session is gone/detached).
+   */
+  function handleHookEvent(sessionId: string, status: ClaudeStatus, detail?: string): void {
+    const session = sessions.get(sessionId);
+    if (session === undefined) return;
+    session.claudeStatus = status;
+    sendIfOpen(
+      session.attachedWs,
+      detail !== undefined ? { type: 'status', status, detail } : { type: 'status', status },
+    );
+  }
+
   /**
    * Reclaim detached sessions whose liveness window has expired (M3).
    *
@@ -159,5 +180,5 @@ export function createSessionManager(cfg: Config): SessionManager {
     sessions = new Map();
   }
 
-  return { handleAttach, get, reapIdle, shutdown };
+  return { handleAttach, get, handleHookEvent, reapIdle, shutdown };
 }

src/session/session.ts

@@ -58,17 +58,26 @@ export function createSession(
   now: number,
   onExit: (session: Session) => void,
 ): Session {
+  // Generate the id first so it can be injected into the shell env: Claude Code
+  // hooks running inside this shell read $WEBTERM_SESSION to tell us which tab
+  // an event belongs to, and POST to $WEBTERM_HOOK_URL (H2).
+  const id = randomUUID();
+
   // M4: let a spawn failure (e.g. missing shell) propagate synchronously.
   const pty: IPty = spawn(cfg.shellPath, [], {
     name: 'xterm-256color',
     cols: dims.cols,
     rows: dims.rows,
     cwd: cfg.homeDir,
-    env: process.env,
+    env: {
+      ...process.env,
+      WEBTERM_SESSION: id,
+      WEBTERM_HOOK_URL: `http://127.0.0.1:${cfg.port}/hook`,
+    },
   });
 
   const meta: SessionMeta = {
-    id: randomUUID(),
+    id,
     createdAt: now,
     shellPath: cfg.shellPath,
   };
@@ -81,6 +90,7 @@ export function createSession(
     lastOutputAt: now,
     exitedAt: null,
     exitCode: null,
+    claudeStatus: 'unknown',
     pty,
   };