[cherry-pick][release-2.40.0][Fixes #21941] Fix no output timestamp case

[pabloem]

• fix no output timestamp case

• revert unnecessary file

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[pabloem]

@reuvenlax @tvalentyn can you please confirm that this should be part of 2.40.0?

[pabloem]

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[reuvenlax]

@pabloem Should ideally be part of 2.40.0, as it fixes a regression in that release.

[pabloem]

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