He is eating snack while he is watching TV.

While he is watching TV, he is eating snack.

-> Watching TV, he is eating snack.

I know that I can emit 'While' and 'he' but there is still a comma between TV and he is.

He is eating snack while he is watching TV.

-> He is eating snack watching TV.

-> He is eating snack, watching TV.

And then I was wondering if there should be a comma or not in the sentence above.

The original sentence has no comma because 'the while conjunction' is written behind and then, should there not be a comma in the omitted sentence, either?

Or are both fine to use or is the one without a comma correct?

What do you native English speakers think?

Thank you so much as usual in advance!