Offer a Continue link for ongoing games in the lobby

A player who accidentally closes the game page can now get back to it
from the lobby.

Backend:
- GameStore.list_ongoing() returns live unfinished sessions (newest
  first), skipping expired keys and finished matches;
- GET /api/me/games lists the games the caller is seated in, with the
  game name/description, players, open seats and your seat (no join
  code);
- store, platform route and app integration tests.

Frontend:
- MyGame/MyGamesPage model plus api::my_games();
- the lobby shows a "Your games" card with phase, seats, players and a
  Continue button linking to /game/<id>; hidden when empty or logged
  out.

server/packages/tavolo-platform/tests/test_store.py

@@ -4,6 +4,7 @@ from __future__ import annotations
 import asyncio
 import time
 import unittest
+from datetime import datetime, timezone
 from typing import Any, Optional, cast
 
 from tavolo.platform import GameSession, Seat
@@ -48,7 +49,7 @@ class _FakePipeline:
         return False
 
     def set(self, key: str, value: str, ex: object = None) -> None:
-        self._ops.append(("set", key))
+        self._ops.append(("set", key, value))
 
     def zadd(self, key: str, mapping: dict) -> None:
         self._ops.append(("zadd", key, mapping))
@@ -88,6 +89,14 @@ class _FakeRedis:
     async def zrem(self, key: str, member: str) -> int:
         return cast(int, self.apply(("zrem", key, member)))
 
+    async def get(self, key: str) -> object:
+        return self.keys.get(key)
+
+    async def zremrangebyscore(
+        self, key: str, minimum: object, maximum: object
+    ) -> int:
+        return cast(int, self.apply(("zremrangebyscore", key)))
+
     async def zrange(
         self,
         name: str,
@@ -113,7 +122,7 @@ class _FakeRedis:
     def apply(self, op: tuple) -> object:
         name, *args = op
         if name == "set":
-            self.keys[args[0]] = "payload"
+            self.keys[args[0]] = args[1]
             return True
         if name == "zadd":
             self.zsets.setdefault(args[0], {}).update(args[1])
@@ -247,6 +256,28 @@ class InMemoryGameStoreTest(unittest.TestCase):
         await store.save(other)
         self.assertEqual(0, await store.count_ongoing())
 
+    @async_test
+    async def test_list_ongoing_newest_first_and_unfinished_only(self) -> None:
+        store = InMemoryGameStore(_registry())
+        old = _session("old", "CODE01")
+        old.created_at = datetime(2026, 1, 1, tzinfo=timezone.utc)
+        new = _session("new", "CODE02")
+        new.created_at = datetime(2026, 1, 2, tzinfo=timezone.utc)
+        await store.save(old)
+        await store.save(new)
+
+        self.assertEqual(
+            ["new", "old"], [s.id for s in await store.list_ongoing()]
+        )
+        self.assertEqual(
+            ["new"], [s.id for s in await store.list_ongoing(limit=1)]
+        )
+
+        # A finished match retained for the final board is not listed.
+        new.state["finished"] = True
+        await store.save(new)
+        self.assertEqual(["old"], [s.id for s in await store.list_ongoing()])
+
     @async_test
     async def test_deadline_queue(self) -> None:
         store = InMemoryGameStore(_registry())
@@ -311,6 +342,33 @@ class RedisGameStoreTest(unittest.TestCase):
         self.assertEqual(1, await store.count_ongoing())
         self.assertNotIn("stale", redis.zsets[ONGOING_GAMES_KEY])
 
+    @async_test
+    async def test_list_ongoing_loads_unfinished_sessions(self) -> None:
+        redis = _FakeRedis()
+        store = RedisGameStore(redis, _registry(), ttl_seconds=3600)  # type: ignore[arg-type]
+        old = _session("old", "CODE01")
+        old.created_at = datetime(2026, 1, 1, tzinfo=timezone.utc)
+        new = _session("new", "CODE02")
+        new.created_at = datetime(2026, 1, 2, tzinfo=timezone.utc)
+        await store.save(old)
+        await store.save(new)
+
+        self.assertEqual(
+            ["new", "old"], [s.id for s in await store.list_ongoing()]
+        )
+        self.assertEqual(
+            ["new"], [s.id for s in await store.list_ongoing(limit=1)]
+        )
+
+        # A finished match retained for the final board is not listed.
+        new.state["finished"] = True
+        await store.save(new)
+        self.assertEqual(["old"], [s.id for s in await store.list_ongoing()])
+
+        # An ongoing entry whose game key expired is skipped.
+        redis.zsets[ONGOING_GAMES_KEY]["gone"] = time.time() + 100
+        self.assertEqual(["old"], [s.id for s in await store.list_ongoing()])
+
     @async_test
     async def test_due_deadlines_uses_zrange_byscore(self) -> None:
         redis = _FakeRedis()