If you don't pick up the Heart Container from a Divine Beast, it will appear outside

Once you activate the Main Control Unit, the Divine Beast in question will move to a different place and start aiming its laser at Hyrule Castle. At this point in the story, it becomes impossible to re-enter the Divine Beast, which would normally render the Heart Container inaccessible.

To prevent this, the devs made it so that the Heart Container appears somewhere close to the Divine Beast for the player to pick up. In all cases, the Heart Container will be within sight range of the travel gate, so if you warp to one of the beasts you only need to look around.

PS: The screenshot is from an old challenge run in which I tried to beat as much of the game as possible without upgrades, hence the “???” item name. After Link has upgraded health at least once, this little box will properly display the item name instead of the question marks.