Beyond knowing they came from God's Spirit, you can't even prove who wrote Hebrews to know who's 'personal lines' they are.
Do you not think God recognizes the kingdom as His Son's? It belongs to Christ. He is the King of His Kingdom. Jesus is Lord.
The book of Hebrews points out the differences in the Old Covenant and the perfect New Covenant. There's no wonder why there would be many references to the Hebrew Scriptures and the fulfillment of the law therein that Jesus the Christ fulfilled.
The only dif between the old and new covenants is FAITH in Jesus replaced the sacrificial system that was previously used by Israel to atone for sin as Jesus was the final sacrifice. This specific part of the Law of Moses was nailed to the cross (Col 2:14) But God's 10C Law remains forever.