Avoid recalculating CheckInfo in generate_castling()

No functional change.
Distribute part of first move time to other moves

Passed both short TC:
LLR: 2.97 (-2.94,2.94) [-1.50,4.50]
Total: 18907 W: 3475 L: 3322 D: 12110

And long TC:
LLR: 2.96 (-2.94,2.94) [0.00,6.00]
Total: 19044 W: 2997 L: 2811 D: 13236

bench: 8430785