Implement client-side prediction with input broadcasting

Reduces perceived lag over internet by broadcasting player inputs immediately
and predicting next positions on all clients before server update arrives.

Protocol changes:
- Added PLAYER_INPUT message type for broadcasting inputs
- Server broadcasts player inputs to all clients on every MOVE message
- Includes player_id, current direction, and full input_buffer (max 3)

Desktop client (Python):
- Tracks input buffers and predicted head positions for all players
- On PLAYER_INPUT: predicts next head position using buffered input
- On STATE_UPDATE: clears predictions, uses authoritative state
- Renderer draws predicted positions with darker color (60% brightness)

Web client (JavaScript):
- Same prediction logic as desktop client
- Added darkenColor() helper for visual differentiation
- Predicted heads shown at 60% brightness

Benefits:
- Instant visual feedback for own movements (no round-trip wait)
- See other players' inputs before server tick (better collision avoidance)
- Smooth experience bridging input-to-update gap
- Low bandwidth (only direction tuples, not full state)
- Backward compatible (server authoritative, old clients work)

All 39 tests passing.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

src/shared/protocol.py

@@ -21,6 +21,7 @@ class MessageType(Enum):
     GAME_STARTED = "GAME_STARTED"
     GAME_OVER = "GAME_OVER"
     ERROR = "ERROR"
+    PLAYER_INPUT = "PLAYER_INPUT"  # Broadcast player input for prediction
 
 
 class Message:
@@ -114,3 +115,18 @@ def create_game_over_message(winner_id: str = None) -> Message:
 def create_error_message(error: str) -> Message:
     """Create an ERROR message."""
     return Message(MessageType.ERROR, {"error": error})
+
+
+def create_player_input_message(player_id: str, direction: tuple, input_buffer: list) -> Message:
+    """Create a PLAYER_INPUT message for client-side prediction.
+
+    Args:
+        player_id: ID of the player who sent the input
+        direction: Current direction tuple
+        input_buffer: List of buffered direction tuples (max 3)
+    """
+    return Message(MessageType.PLAYER_INPUT, {
+        "player_id": player_id,
+        "direction": direction,
+        "input_buffer": input_buffer
+    })