The very recipients of the book speak against Pauline authorship…to the Hebrews. Paul was apostle to the Gentiles, to whom many of his letters were addressed, and his letters to them were sent to destinations in the empire, not to Jerusalem.
The Lukan connection is far too circumstantial and conjectural. Dissimilarity of writing style between Hebrews and Paul’s other letters simply suggests different authorship. The mention of Timothy says little, Timothy being known amongst other potential writers within his orbit. EGW also postulates a 6,000 year old earth. She is not the last word on biblical interpretation.
The greeting in chapter 13 makes no sense as a Pauline identification. He was viewed with suspicion in Jerusalem, the likely location of the recipients considering the focus on temple services and priesthood. Paul served no congregations there, and was actually viewed with suspicion by the Jewish Christians there for his radical views on the role of the Torah.
Finally, Hebrews contains no positive self identification of Paul in its opening. This is unlike every other authentic Pauline letter in the NT.