This problem has been solved.

I jumped out of the limitation of Qt (getNativeHandle) and directly used the interface provided by EGL to obtain the context and display (eglGetCurrentDisplay/eglGetCurrentContext) in the context state created by Qt.

makeQtCurrent();
auto eglDisplay = eglGetCurrentDisplay();
auto eglContext = eglGetCurrentContext();
doneQtCurrent():

I have checked Qt documentation, and in fact, I am using Qt 5, which does not yet support QNativeInterface::QEGLContext.