Your problem has nothing to do with SerializeField. Are you aware what SerializeField do? SerializeField in Unity used for reflecting object value to Unity Editor Inspector. It doesn't affect variable protection level. When you didn't assign any protection accessors (private, public, internal), it is private as default. So only accesible in this class level. If you want to access it from another class, you should just add public accessor.
public AudioSource audioSrc;
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