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I am informed the typical usage of "wake", that is "wake up"

Cambridge Dictionary

I woke up with a headache

I guess both of these are correct

I had a massage yesterday which really helped me to fall asleep. When I woke up I felt I was full of energy.

... When I woke back up I felt I was full of energy.

A native speaker told me, the latter sounds more natural, why is that?

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Your native speaker misled you. (Native speakers get things wrong all the time!)

To insert back is possible but unnecessary and definitely not more natural.

People always wake again in the sense that they were awake before they fell asleep. To add again is unnecessary. So is to add up to woke.

So you either just woke/awoke or you woke up or woke up again.

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Back can be used as an adverb, and it can mean a few things. One meaning is to emphasize that an action is returning something back to a normal state, after being in an alternate state temporarily.

I put the paper back in the tray (it was temporary out of the tray)

I got my dog back from the vet (dog was temporarily at the vet)

I woke back up at 6:00 because someone was banging on my door (you probably fell asleep at 5:30 or otherwise were only sleeping for a short time).

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