fix(offline): give the local human seat the real account id

In a local game the human seat's account id was a synthetic 'local:human:0',
so seatName's `accountId === session.userId` check never matched: the game
header rendered BOTH seats as 🤖 (the vs_ai fallback), and the lobby's
groupGames could not find the viewer's seat, so a human's turn read as
'Their turn' with the hourglass. Carry the real account id on the human seat
(create -> record -> GameView); the robot keeps its synthetic id.

Local games created before this fix keep the old display (no migration).

ui/src/lib/localgame/serialize.ts

@@ -17,6 +17,9 @@ import type { Variant } from '../model';
 export interface Seat {
   kind: 'human' | 'robot';
   name: string;
+  /** The player's real account id for a human seat, so the client identifies "you" and the correct
+   *  turn exactly as in an online game; absent for the robot (a synthetic id is derived). */
+  accountId?: string;
 }
 
 /** LocalGameRecord is the durable form of one local game — everything needed to reconstruct it. */

ui/src/lib/localgame/source.list.test.ts

@@ -51,6 +51,20 @@ describe('LocalSource.list', () => {
     expect(list.every((g) => g.vsAi && g.status === 'active')).toBe(true);
   });
 
+  it('carries the human seat account id into the GameView so the client identifies "you"', async () => {
+    const src = new LocalSource();
+    await src.create({
+      ...opts('local:me', 3n),
+      seats: [
+        { kind: 'human', name: 'You', accountId: 'acct-42' },
+        { kind: 'robot', name: 'Robot' },
+      ],
+    });
+    const [g] = await src.list();
+    expect(g.seats[0].accountId).toBe('acct-42'); // the human's real id, matched against the session
+    expect(g.seats[1].accountId).not.toBe('acct-42'); // the robot keeps a synthetic id
+  });
+
   it('reconstructs a game persisted by a previous session (not in the source cache)', async () => {
     // Seed the store via one source, then list from a fresh source whose in-memory cache is empty.
     await new LocalSource().create(opts('local:old', 7n));

ui/src/lib/localgame/source.ts

@@ -120,7 +120,7 @@ export class LocalSource implements GameLoopSource {
     const now = nowUnix();
     const record = serializeGame(game, {
       id: opts.id,
-      seats: opts.seats.map((s) => ({ kind: s.kind, name: s.name })),
+      seats: opts.seats.map((s) => ({ kind: s.kind, name: s.name, accountId: s.accountId })),
       createdAtUnix: now,
       updatedAtUnix: now,
       robotLastMoveAtUnix: now,
@@ -341,7 +341,7 @@ export class LocalSource implements GameLoopSource {
     const { game, record } = entry;
     const seats: Seat[] = record.seats.map((s, i) => ({
       seat: i,
-      accountId: `${LOCAL_ID_PREFIX}${s.kind}:${i}`,
+      accountId: s.accountId ?? `${LOCAL_ID_PREFIX}${s.kind}:${i}`,
       displayName: s.name,
       score: game.scoreOf(i),
       hintsUsed: 0,