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/tests/test_routes_games.py

@@ -236,6 +236,52 @@ class GamesRouteTest(unittest.TestCase):
             self.assertEqual(400, text.status_code)
             self.assertEqual(400, huge.status_code)
 
+    @async_test
+    async def test_my_games_lists_my_ongoing_games(self) -> None:
+        transport = ASGITransport(app=app)
+        async with AsyncClient(transport=transport, base_url="http://127.0.0.1") as client:
+            with oidc_user("alice"):
+                created = await client.post(
+                    "/api/games", json={"game_type": "briscola"}
+                )
+            game_id = created.json()["id"]
+
+            with oidc_user("alice"):
+                listed = await client.get("/api/me/games")
+            self.assertEqual(200, listed.status_code)
+            # The app suite shares one in-memory store, so other tests'
+            # games may be listed too: pick ours by id.
+            by_id = {g["id"]: g for g in listed.json()["results"]}
+            self.assertIn(game_id, by_id)
+            entry = by_id[game_id]
+            self.assertEqual("briscola", entry["game_type"])
+            self.assertEqual("Briscola", entry["game_name"])
+            self.assertTrue(entry["game_description"])
+            self.assertEqual("lobby", entry["phase"])
+            self.assertEqual(1, entry["seats_open"])
+            self.assertEqual(0, entry["your_seat"])
+            self.assertNotIn("join_code", entry)
+
+            # A logged-in non-player does not see the game.
+            with oidc_user("mallory"):
+                others = await client.get("/api/me/games")
+            self.assertNotIn(
+                game_id, [g["id"] for g in others.json()["results"]]
+            )
+
+            # Once the match starts it stays listed, for both players.
+            code = created.json()["join_code"]
+            with oidc_user("bob"):
+                await client.post("/api/games/join", json={"code": code})
+            with oidc_user("bob"):
+                started = await client.get("/api/me/games")
+            bob_entry = next(
+                g for g in started.json()["results"] if g["id"] == game_id
+            )
+            self.assertEqual("playing", bob_entry["phase"])
+            self.assertEqual(1, bob_entry["your_seat"])
+            self.assertEqual(0, bob_entry["seats_open"])
+
     @async_test
     async def test_get_unknown_game(self) -> None:
         transport = ASGITransport(app=app)