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/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,
   };