Out of Burnes, Woodruff and Hader, I wouldn't be surprised at all if Josh is the one who is kept just because even as thee best reliever in the game he will still likely be cheaper to extend or in FA than Corbin/Brandon.
My favorite Hader stat is that since 2017 he has the 3rd highest Win Probability Added in MLB. Not among relievers, among all pitchers. Only Scherzer and deGrom are higher & depending on how long Jacob (+15.81 WPA) is injured, Josh (+14.49 WPA) could pass him this year too.