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>

web/protocol.js

@@ -17,7 +17,8 @@ const MessageType = {
     PLAYER_LEFT: 'PLAYER_LEFT',
     GAME_STARTED: 'GAME_STARTED',
     GAME_OVER: 'GAME_OVER',
-    ERROR: 'ERROR'
+    ERROR: 'ERROR',
+    PLAYER_INPUT: 'PLAYER_INPUT'  // Broadcast player input for prediction
 };
 
 class Message {