Distinct study plan days and steadier battles

What changed

• Each day in the day-by-day study plans now has its own problems that match what the day teaches, with no repeats. The last day is harder and mixes topics.
• Players no longer look disconnected to their opponent mid-battle, and Cancel Search in the battle lobby leaves the queue right away. Practice problems also open faster.
• The model leaderboard now shows how much of the final code each model wrote, puts every score on the same scale, and fits on phones. The Builder model picker lists the Agentic+ models on every plan, with a lock that links to plans when yours does not include them.