Add player turn information to Breakthrough's serialization and deserialization function #1627

Job	Run time
build (ubuntu-24.04, 3.12, OFF, OFF, OFF)	18m 14s
build (macos-14, 3.12, OFF, OFF, OFF)	8m 27s
build (ubuntu-22.04, 3.11, ON, OFF, OFF)	22m 21s
build (ubuntu-22.04, 3.10, ON, OFF, ON, https://github.com/google/or-tools/releases/download/v9.6...	19m 49s
build (ubuntu-22.04, 3.10, OFF, OFF, OFF)	17m 34s
build (macos-13, 3.11, 0, OFF, OFF, OFF)	21m 30s
	1h 47m 55s

Provide feedback