The Heavy Phaser Assault Platform is supposed to be available for use on temporal battlecruisers (per console descriptors), but it can't be used on the Typhoon Temporal Battlecruiser. I'm hoping this is just a minor glitch with the release of the Typhoon.
Comments
The Paladin & Ranger classes are both "Temporal Battlecruisers" with a Temporal Spec, whereas the Typhoon is a regular "Battlecruiser" with Temporal Spec.
Thus, WAI, the HPAP correctly cannot be equipped on the Typhoon.
(If the Paladin & Ranger were to have the name of the Spec in the ship name, they'd become "Temporal Temporal Battlecruisers".)
The Paladin, which this console comes from, is a full-and-proper "Temporal Battlecruiser" which also has the Temporal Spec but calling it a 'Temporal Temporal Battlecruiser' would be silly.
The Typhoon is a Temporal Battlecruiser, but not a Temporal Battlecruiser
Similarly, the Kuthar is a Pilot Escort but is not a Pilot Escort, and thus cannot equip the Pilot Escort consoles. (It can equip the Tier 5 Andorian Consoles, though.)
Again, the Legendary Bortasqu' is a Command Battlecruiser, but is not a Command Battlecruiser, so cannot equip the Command Battlecruiser consoles.
I have tried to help you understand the distinction and difference between the two types of ship despite the naming convention making them look the same, even though they are different. I have given you two other examples, but there's plenty more ships in the game with naming similarities such as those given above. This does not mean that consoles from one kind of ship should be equippable on others.