feat(snake): optimize duels and persist customizations

- Add deadline-aware iterative duel search with bitboards and tuple bodies.

- Reuse transposition bounds and move-order hints across search depths.

- Persist snake colors, heads, and tails in SQLite and PostgreSQL.

- Restore customization metadata when hydrating dashboard replays.

- Cover duel deadlines, cache reuse, schema storage, and replay output.

server/database/normalized_turn.py

@@ -27,6 +27,7 @@ def hydrate_replay_turns(game_row, turn_rows, snake_rows, decode_json:Callable)
     api_snakes = []
     for snake_row in rows_by_turn.get(turn, []):
       body = decode_json(snake_row["body_json"]) or []
+      customizations = decode_json(snake_row["customizations_json"]) or {}
       api_snake = {
         "id": snake_row["snake_id"],
         "name": snake_row["snake_name"],
@@ -34,6 +35,7 @@ def hydrate_replay_turns(game_row, turn_rows, snake_rows, decode_json:Callable)
         "length": snake_row["length"],
         "head": {"x": snake_row["head_x"], "y": snake_row["head_y"]},
         "body": body,
+        "customizations": customizations,
       }
       if snake_row["latency"] is not None:
         api_snake["latency"] = snake_row["latency"]
@@ -45,6 +47,7 @@ def hydrate_replay_turns(game_row, turn_rows, snake_rows, decode_json:Callable)
         "length": snake_row["length"],
         "head": api_snake["head"],
         "body": body,
+        "customizations": customizations,
         "is_you": bool(snake_row["is_you"]),
         "inferred_move": snake_row["inferred_move"],
         "latency": snake_row["latency"],