And being made perfect - That is, being made a “complete” Saviour - a Saviour suited in all respects to redeem people. Sufferings were necessary to the “completeness” or the “finish” of his character as a Saviour, not to his moral perfection, for he was always without sin; see this explained in the notes on Hebrews 2:10.
He became the author - That is, he was the procuring cause (αἴτιος aitios) of salvation. It is to be traced wholly to his sufferings and death; see the note, Hebrews 2:10. “Unto all them that obey him.” It is not to save those who live in sin. Only those who “obey” him have any evidence that they will be saved; see the note, John 14:15.