Add game end status with an end_game DM tool and automatic 0-HP detection

Games now have a status/ended_reason pair. The DM can call the new
end_game tool when the story reaches a real conclusion (victory,
defeat, or a resolved one-shot), and the backend independently ends
the game whenever a character's HP drops to 0 or below, regardless of
whether the DM narrates it. The frontend shows a banner and a
"Beendet" badge once a game ends.

HP moves from the freeform combat_stats bag into dedicated
current_hp/max_hp columns on Character, since reliably detecting 0 HP
requires a real integer rather than parsing strings like "3/10" out of
an LLM-authored key/value dict. Also fixed combat_stats to fully
replace on each upsert instead of merging, matching its documented
contract — the merge was leaving stale keys (old HP/TP text) behind
after the model stopped sending them.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

backend/app/api/routes_games.py

@@ -71,6 +71,8 @@ async def _serialize_games(
                 created_at=game.created_at,
                 is_participant=is_participant,
                 my_character_id=viewer_participation.get(game.id),
+                status=game.status,
+                ended_reason=game.ended_reason,
             )
         )
     return result

backend/app/api/ws_game.py

@@ -123,9 +123,16 @@ async def game_websocket(websocket: WebSocket, game_id: uuid.UUID, ticket: str)
                     async def _broadcast_roll(notation: str) -> None:
                         await manager.broadcast(game_id, {"type": "rolling", "notation": notation})
 
+                    async def _broadcast_game_ended(reason: str) -> None:
+                        await manager.broadcast(game_id, {"type": "game_ended", "reason": reason})
+
                     try:
                         dm_message = await run_dm_turn(
-                            session, game_id, latest_player_message=content, on_roll=_broadcast_roll
+                            session,
+                            game_id,
+                            latest_player_message=content,
+                            on_roll=_broadcast_roll,
+                            on_game_ended=_broadcast_game_ended,
                         )
                     except Exception:  # noqa: BLE001
                         logger.exception("DM turn failed for game %s", game_id)