He did die in the original Modern Warfare 2 (2009), but Modern Warfare (2024) (and its sequel that just released, Modern Warfare II (2024)) is a reboot that's set in a different timeline, completely separate from the original trilogy.

Ghost is the only one allowed to call Soap Johnny, because they're boyfriends. While the campaign teases us with brief exchanges between the two hunks throughout, it isn't until the final act that things really start heating up. Alone is when it all starts to go wrong for our heroes.