chore(v3): remove no-private-header flag (#15863) #1026

Job	Run time
debug_job	2s
Save PR ref	2s
Windows-Bazel / bazel + msvc-2022 + opt + Core	25s
macOS-Bazel	0s
macOS-CMake	0s
Windows-CMake	0s
Notify-Google-Chat	2s
	31s

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