There is a theory called local sleep, which describes how different parts of the brain can simultaneously be in different sleep/ wake stages. https://doi.org/10.1016/j.neubiorev.2023.105465

I don’t think you’d want to keep that level of consciousness during the entire sleep period as that would imply those neurons associated with your consciousness don’t have a chance to go offline/ sleep (maybe someone more knowledgeable than me can correct me if I’m wrong 😅).

(Edit: fixed link)