Yeah it's only available in Stormblood and Shadowbringers areas - where you can dive underwater it will be allowed automatically (there is no visual indication to that effect on the map as far as I know, but it's usually pretty clear where you can dive and swim underwater), but to actually take a mount underwater with you requires you to unlock flight in that zone first (mount diving is unlocked at the same time). And the story will require you to go underwater at times in the revelant areas too so don't feel you'll miss out on anything cool!