A justice or judge of the United States before whom a habeas corpus proceeding is pending, may, before final judgment or after final judgment of discharge, or pending appeal, stay any proceeding against the person detained in any State court or by or under the authority of any State for any matter involved in the habeas corpus proceeding.

For purposes of this section, a habeas corpus proceeding is not pending until the application is filed.

If a State prisoner sentenced to death applies for appointment of counsel pursuant to section 3599(a)(2) of title 18 in a court that would have jurisdiction to entertain a habeas corpus application regarding that sentence, that court may stay execution of the sentence of death, but such stay shall terminate not later than 90 days after counsel is appointed or the application for appointment of counsel is withdrawn or denied.