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/README.md

@@ -279,6 +279,7 @@ All endpoints except `/api/health`, `/api/docs`, `/api/openapi.json`,
 | `POST` | `/api/games/join` | Join with `{"code": "ABC123"}`. The last player triggers the start and gets the game view back |
 | `GET` | `/api/games/preview?code=ABC123` | Pre-join summary of the lobby behind a code: game name/description, seated players, open seats and the engine-echoed options. `404` when the code is unknown |
 | `GET` | `/api/games/{id}` | Game snapshot. Seated players get the personalized view (own hand plus the join code); anyone else gets the read-only spectator view: table, scores, captured counts and scope, no hands and no join code |
+| `GET` | `/api/me/games` | Live games the caller is seated in (waiting lobbies, matches in progress or between hands), newest first, for the lobby's "Continue" list. Finished matches are not included |
 | `GET` | `/api/me/matches` | Cursor-paginated match history with the engine's `result` and per-player Elo deltas (`?limit=&cursor=&game_type=`) |
 | `GET` | `/api/me/ratings` | The caller's Elo rating per game type |
 | `GET` | `/api/leaderboard` | Elo rating, aggregated wins / matches / points per player, sorted by Elo (`?game_type=`) |