feat(v0.4): multi-device session sharing (backend)

Relax the one-WS-per-session invariant (#5) so multiple devices mirror the
same live terminal (everyone sees output, anyone can type — tmux-style).

- types.ts: Session.attachedWs → clients Set + clientDims Map; add cwd;
  SessionManager.list() + LiveSessionInfo
- session.ts: broadcast() output/exit to all clients; attachWs JOINS (no kick,
  takes dims); detachWs removes one client, stamps detachedAt only when the last
  leaves; setClientDims resizes PTY to the MIN cols/rows across clients
- manager.ts: join instead of kick; broadcast status; onExit drops only when a
  client was attached; list() for discovery
- server.ts: GET /live-sessions; resize → per-client setClientDims; close →
  detach one client; permission gate uses clients.size
- tests: rewrote session/manager tests for multi-client (join/broadcast/min-dims/
  last-detach) + list(); 222 pass, tsc clean

src/types.ts

@@ -140,9 +140,15 @@ export interface SessionMeta {
 export interface Session {
   readonly meta: SessionMeta;
   readonly buffer: RingBuffer;
-  /** attached ws, or null = detached but PTY still alive (vibe-coding core). */
-  attachedWs: WebSocketLike | null;
-  detachedAt: number | null; // detach time
+  /** All currently-attached clients (multi-device mirror sharing). Empty set =
+   *  detached but PTY still alive (vibe-coding core). Output/exit/status are
+   *  broadcast to every client; any client can send input (shared control). */
+  readonly clients: Set<WebSocketLike>;
+  /** Per-client requested terminal dims; the PTY uses the MIN cols/rows across
+   *  all clients (tmux-style) so every device sees content without overflow. */
+  readonly clientDims: Map<WebSocketLike, Dims>;
+  /** Time the LAST client left (clients became empty); null while ≥1 attached. */
+  detachedAt: number | null;
   /** last pty.onData timestamp; reapIdle liveness proxy (M3). */
   lastOutputAt: number;
   /** PTY exit time; null = alive. Once set: writeInput/resize are ignored (L4),
@@ -151,6 +157,8 @@ export interface Session {
   exitCode: number | null;
   /** Claude Code activity from hooks (H2); updated by manager.handleHookEvent. */
   claudeStatus: ClaudeStatus;
+  /** Spawn directory, for the /live-sessions label; null when unknown. */
+  cwd: string | null;
   /** tmux session name (H1) when running under tmux, else null. */
   readonly tmuxName: string | null;
   readonly pty: IPty;
@@ -159,14 +167,24 @@ export interface Session {
 // impl anchors [src/session/session.ts]:
 //   createSession(cfg: Config, dims: Dims, now: number, onExit: (s: Session) => void): Session
 //                                                  // spawn failure THROWS, not swallowed (M4)
-//   attachWs(session: Session, ws: WebSocketLike): WebSocketLike | null   // returns kicked old ws
-//   detachWs(session: Session, now: number): void                        // never kills PTY
-//   writeInput(session: Session, data: string): void                     // no-op after exit (L4)
-//   resize(session: Session, cols: number, rows: number): void           // no-op after exit; idempotent
+//   attachWs(session: Session, ws: WebSocketLike, dims: Dims): void  // adds a client, replays buffer (no kick)
+//   detachWs(session: Session, ws: WebSocketLike, now: number): void // removes one client; never kills PTY
+//   writeInput(session: Session, data: string): void                // no-op after exit (L4)
+//   setClientDims(session: Session, ws: WebSocketLike, cols, rows): void  // PTY = min over clients (L4 no-op after exit)
 //   kill(session: Session): void
 
 /* ──────────────────────── manager (§3.5) ─────────────────────── */
 
+/** A live (or just-exited) server session, for the /live-sessions discovery list. */
+export interface LiveSessionInfo {
+  id: string;
+  createdAt: number;
+  clientCount: number; // how many devices are currently attached
+  status: ClaudeStatus;
+  exited: boolean;
+  cwd: string | null;
+}
+
 export interface SessionManager {
   handleAttach(
     ws: WebSocketLike,
@@ -176,6 +194,8 @@ export interface SessionManager {
     cwd?: string,
   ): Session;
   get(id: string): Session | undefined;
+  /** Live sessions for multi-device discovery (newest first). */
+  list(): LiveSessionInfo[];
   /** Set a session's Claude status (from a hook) and push it to the attached ws (H2/H3). */
   handleHookEvent(
     sessionId: string,