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.

tests/test_GameplayDatabase.py

@@ -13,6 +13,11 @@ class TestGameplayDatabase(unittest.IsolatedAsyncioTestCase):
         "name": "Me",
         "health": 90,
         "length": 3,
+        "customizations": {
+          "color": "#00ff00",
+          "head": "ferret",
+          "tail": "swirl",
+        },
         "head": {"x": me_head[0], "y": me_head[1]},
         "body": [
           {"x": me_head[0], "y": me_head[1]},
@@ -99,10 +104,13 @@ class TestGameplayDatabase(unittest.IsolatedAsyncioTestCase):
       """, ("game-abc", 2, "me")).fetchone()[0]
       self.assertNotEqual(stored_body, "[]")
       identities = connection.execute("""
-        SELECT snake_id, snake_name, is_you FROM game_snakes
+        SELECT snake_id, snake_name, is_you, customizations_json FROM game_snakes
         WHERE game_id = ? ORDER BY snake_id
       """, ("game-abc",)).fetchall()
-      self.assertEqual(identities, [("enemy", "Enemy", 0), ("me", "Me", 1)])
+      self.assertEqual(identities, [
+        ("enemy", "Enemy", 0, "{}"),
+        ("me", "Me", 1, '{"color":"#00ff00","head":"ferret","tail":"swirl"}'),
+      ])
       repeated_identity = connection.execute("""
         SELECT snake_name, is_you FROM snake_turns
         WHERE game_id = ? AND turn = ? AND snake_id = ?
@@ -127,7 +135,15 @@ class TestGameplayDatabase(unittest.IsolatedAsyncioTestCase):
       self.assertEqual(replay["turns"][1]["my_thinking"]["reason"], "food")
       self.assertEqual(replay["turns"][1]["food"], [{"x": 2, "y": 2}])
       self.assertEqual(replay["turns"][1]["you"]["id"], "me")
-      self.assertEqual(len(replay["turns"][1]["snakes"][0]["body"]), 3)
+      me = next(snake for snake in replay["turns"][1]["snakes"] if snake["snake_id"] == "me")
+      self.assertEqual(me["customizations"], {
+        "color": "#00ff00",
+        "head": "ferret",
+        "tail": "swirl",
+      })
+      self.assertEqual(len(me["body"]), 3)
+      api_me = next(snake for snake in replay["turns"][1]["board"]["snakes"] if snake["id"] == "me")
+      self.assertEqual(api_me["customizations"], me["customizations"])
 
       connection.close()