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_routes.py

@@ -188,6 +188,63 @@ class GamesRouteTest(unittest.TestCase):
                 response = await client.get("/api/games/does-not-exist")
             self.assertEqual(404, response.status_code)
 
+    @async_test
+    async def test_my_games_lists_only_my_ongoing_games(self) -> None:
+        app, platform, _ = make_platform()
+        transport = ASGITransport(app=app)
+        async with AsyncClient(transport=transport, base_url="http://127.0.0.1") as client:
+            anonymous = await client.get("/api/me/games")
+            self.assertEqual(401, anonymous.status_code)
+
+            with oidc_user(platform.oidc, "alice"):
+                mine = await client.post(
+                    "/api/games", json={"options": {"target": 5}}
+                )
+            with oidc_user(platform.oidc, "bob"):
+                theirs = await client.post("/api/games", json={})
+            self.assertEqual(201, mine.status_code)
+            self.assertEqual(201, theirs.status_code)
+
+            with oidc_user(platform.oidc, "alice"):
+                listed = await client.get("/api/me/games")
+            self.assertEqual(200, listed.status_code)
+            results = listed.json()["results"]
+            self.assertEqual([mine.json()["id"]], [g["id"] for g in results])
+            entry = results[0]
+            self.assertEqual("dummy", entry["game_type"])
+            self.assertEqual("Dummy game", entry["game_name"])
+            self.assertTrue(entry["game_description"])
+            self.assertEqual("lobby", entry["phase"])
+            self.assertEqual(5, entry["target"])
+            self.assertEqual(1, entry["seats_open"])
+            self.assertEqual(0, entry["your_seat"])
+            self.assertNotIn("join_code", entry)
+            self.assertEqual("alice", entry["players"][0]["sub"])
+
+            # Bob's own game is the only one he sees; Alice's is not his.
+            with oidc_user(platform.oidc, "bob"):
+                bobs = await client.get("/api/me/games")
+            self.assertEqual(
+                [theirs.json()["id"]],
+                [g["id"] for g in bobs.json()["results"]],
+            )
+
+            # Once Bob joins Alice's game it appears for both, now in the
+            # playing phase.
+            with oidc_user(platform.oidc, "bob"):
+                await client.post(
+                    "/api/games/join", json={"code": mine.json()["join_code"]}
+                )
+            with oidc_user(platform.oidc, "bob"):
+                bobs = await client.get("/api/me/games")
+            by_id = {g["id"]: g for g in bobs.json()["results"]}
+            self.assertEqual(
+                {mine.json()["id"], theirs.json()["id"]}, set(by_id)
+            )
+            self.assertEqual("playing", by_id[mine.json()["id"]]["phase"])
+            self.assertEqual(1, by_id[mine.json()["id"]]["your_seat"])
+            self.assertEqual(0, by_id[mine.json()["id"]]["seats_open"])
+
 
 class GameTypesRouteTest(unittest.TestCase):
     @async_test