On the PS4 cross menu bar (where you launch games), scroll to the ffxiv game picture like you are going to launch the game. Instead of pushing x, push down on the d pad, then push right on the d pad. This will bring you to a bunch of pictures and stuff about the game. scroll down past trophies, friends, and recent activities. as you go past recent activities you will hit view all, scroll down on d pad on more time. Now you're in add on section.

Under add ons, it should say "my add-ons" and there should be heavenward. push x, it will take you to another page with a little download arrow next to FFXIV HW. Push x on it and after about 5 seconds you will see "FFXIV HW added to downloads" thats the 1.7gb patch everyone is missing and the reason your launcher doesn't look right and the reason you can't start the HW quests in game.

Enjoy!