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Why? Data engineers don't do much with data and data scientists learn about machine learning anyways. A machine learning engineer specifically works with neural nets (mind you, some don't but I'd consider those as data scientist)
And an ML scientist is more of a researcher afaik.
I'm guessing your path probs ends up looking like this: DBA, DEng, DA, DSc, MLEng.
Unemployed, living in a stranger's basement.