Phase 2: async play-by-turn — the games ledger and turn signals

The lobby is now the front door to all your games. A "your games"
ledger lists every seat this browser holds — room code, whose turn it
is (including counteraction/discard/interrupt waits, which count as
your turn), the round, and how long since the last move — with
one-click resume, a forget control, and a green highlight when a game
waits on you. The server answers a token-validated myGames query with
per-seat summaries; the client polls every 45 seconds, so turns in
other rooms reach you wherever you are. Turn signals travel three
ways: the tab title flips to "● Your turn", the favicon grows a green
dot, and — opt-in via "notify me on my turn" — a browser notification
fires when a turn becomes yours anywhere. Landing in the app now
shows the ledger rather than teleporting into the last game;
mid-game socket drops still walk straight back to the table.
Verified live: two seeded games, ledger showing "gandalf's turn" and
YOUR TURN, one-click resume into the correct game with history.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

packages/server/src/rooms.ts

@@ -140,6 +140,39 @@ export function runCommand(
   return { events: result.events };
 }
 
+export interface GameSummary {
+  roomId: string;
+  name: PlayerId;
+  players: PlayerId[];
+  started: boolean;
+  finished: boolean;
+  winner: PlayerId | null;
+  activePlayerId: PlayerId | null;
+  yourTurn: boolean;
+  round: number | null;
+  lastMoveAt: string | null;
+}
+
+/** A seat-holder's one-line view of a room, for the lobby ledger. */
+export function summarize(room: Room, playerId: PlayerId): GameSummary {
+  const s = room.state;
+  const active = s && s.phase === "playing" ? s.players[s.turn.activeIndex]!.id : null;
+  const waitingOn = s?.stack?.waitingOn ?? s?.pendingDiscard ?? s?.outOfTurnWindow?.playerId ?? null;
+  const turnHolder = waitingOn ?? active;
+  return {
+    roomId: room.id,
+    name: playerId,
+    players: [...room.players],
+    started: s !== null,
+    finished: s?.phase === "finished",
+    winner: s?.winner ?? null,
+    activePlayerId: active,
+    yourTurn: s?.phase === "playing" && turnHolder === playerId,
+    round: s?.turn.round ?? null,
+    lastMoveAt: room.log.length > 0 ? room.log[room.log.length - 1]!.at : null,
+  };
+}
+
 export function viewForPlayer(room: Room, playerId: PlayerId): GameView | null {
   return room.state ? viewFor(room.state, playerId) : null;
 }