Isn’t the story that Brees officially retired behind the scenes after the 2019 season, it was an unkept secret at the Pro Bowl and it was simply a case of waiting for the official announcement.
Then he heard that Payton wanted Brady to come (and judging by the Miami stuff Brady would have been open to it) and decided he couldn’t watch Brady come and win with his team and stayed one more year.
Ironically Brady beat Brees in his last game in the league and went on to win the Superbowl anyway.