Does the court of appeals have jurisdiction to review a district court's decision that a habeas petitioner's Rule 60(b)(6) motion is an unauthorized second-or-successive habeas petition?

QUESTION PRESENTED Tremane Wood was convicted of felony murder for participating in a robbery in which his older brother, Zjaiton Wood, killed one of the robbery’s victims and confessed to that fact. In separate trials, Mr. Wood was sentenced to death while Zjaiton was sentenced to life without parole. That disparity comes down to resources. Whereas Zjaiton was zealously represented by three experienced capital defense attorneys with Oklahoma’s Indigent Defense System, the trial court appointed private conflict counsel to represent Mr. Wood who was paid just $10,000, did no work on Mr. Wood’s case other than show up for court, and was impaired by an addiction to alcohol, cocaine, and prescription pills. In his federal habeas petition, Mr. Wood raised a claim under Strickland v. Washington, 466 U.S. 668 (1984), based on conflict counsel’s penalty-phase ineffectiveness. When the district court adjudicated that claim, however, it failed to review the last reasoned state court decision adjudicating the claim’s merits—a fact which Respondent did not dispute in the proceedings below—as required by this Court’s decisions in Yist v. Nunnemaker, 501 U.S. 797 (1991), in Wilson v. Sellers, 584 U.S. 122 (2018), and by 28 U.S.C. § 2254(d). Based on that fundamental defect in the district court’s adjudication of his Strickland claim, along with new and various extraordinary circumstances, Mr. Wood moved the district court to reopen the judgment in his habeas proceeding under Federal Rule of Civil Procedure 60(b)(6). Without reaching the Rule 60(b)(6) motion’s merits, the district court decided that it was “not a true Rule 60(b) motion,” rather it was an unauthorized second-orsuccessive habeas petition, and transferred it to the Tenth Circuit under 28 U.S.C § 1631 for authorization under 28 U.S.C. § 2244(b). Mr. Wood timely appealed. Following the court of appeals’ sua sponte request for briefing on whether it has appellate jurisdiction to review the district court’s decision, the court of appeals held that it “lacks jurisdiction to review, via this appeal, the district court’s conclusion that Wood’s Rule 60 motion was an unauthorized second or successive § 2254 petition,” and dismissed Mr. Wood’s appeal. This petition presents the following question: Does 28 U.S.C. § 1291 give a federal court of appeals jurisdiction to review a district court’s decision that a habeas petitioner’s motion under Rule 60(b)(6) of the Federal Rules of Civil Procedure is not a true Rule 60(b) motion if, in the same order, the district court also transfers to the court of appeals under 28 U.S.C. § 1631 what it construes as a habeas petition? i