⚡ Parallelize WebSocket Broadcasts

[WeixuanZ]

Optimized broadcast_filtered_game_states in websocket_manager.py to use asyncio.gather for concurrent message sending.

What:

• Refactored broadcast_filtered_game_states to create a list of async tasks for each connected player.
• Encapsulated per-player sending logic (getting view + sending message + error handling) into an inner send_to_one helper function.
• Executed all tasks concurrently using asyncio.gather.

Why:

• The previous implementation iterated sequentially over active connections. With network latency (even small), the total time to broadcast to all players grew linearly with the number of players.
• For 500 players with 10ms latency, the last player would receive the update 5 seconds after the first player.
• This optimization decouples broadcast time from the number of players (mostly), limiting it to the maximum single-client latency + processing overhead.

Measured Improvement:

• Baseline: ~6.0060 seconds (500 clients, 10ms delay)
• Optimized: ~0.1219 seconds (500 clients, 10ms delay)
• Speedup: ~50x improvement in total broadcast time.

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PR created automatically by Jules for task 11568541175769807919 started by @WeixuanZ

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