You only get 1 bullet/projectile loaded per turn. (1 load 'action')

Once per round, phantom hands load a single ranged weapon or firearm with conjured ammunition. This ammunition counts as magical for overcoming damage reduction and attacking incorporeal creatures, but is the standard for its type (a normal bullet or pellets and black powder in the case of firearms). Conjured ammunition ceases to exist 1 round after it is removed from the weapon, or at the end of the duration, whichever comes first.

The highlighted portion says that it performs a weapon load (action) once per turn.

Now lets take a look at the multishooting weapons: (I'll use double crossbow as an example)

Load: Loading one bolt is a standard action; the Rapid Reload feat reduces this to a move action. Crossbow Mastery allows you to reload both bolts as a single move action.

(again, empahasis mine).

The phantoms hands will load your crossbow once. This load action only loads one bolt at a time.

For early firearms, the same applies:

Early firearms are muzzle-loaded, requiring bullets or pellets and black powder to be rammed down the muzzle. If an early firearm has multiple barrels, each barrel must be loaded separately

If you were using an advanced firearm, you would get the complete capacity.

Advanced firearms are chamber-loaded. It is a move action to load a one-handed or two-handed advanced firearm to its full capacity.

References:

Firearms

double crossbow

No

But the argument is not so straightforward.

The problem with this question is that the RAW are murky enough to allow for some leeway in interpretation. Going by RAI, the intention was clearly to use Two-Weapon Fighting with one-handed weapons, and not game the system by attacking with a versatile weapon while holding it in two hands, arguing that it still counts as a one-handed weapon for the Dual Wielder feat.

The Rules

Dual Wielder

You can use two-weapon fighting even when the one-handed melee weapons you are wielding aren’t light.

While this qualifies the longsword for two-weapon fighting, the Versatile property states that:

Versatile

This weapon can be used with one or two hands. A damage value in parentheses appears with the property—the damage when the weapon is used with two hands to make a melee attack.

This explicitly states the need to use both hands to make a two-handed attack and use the bigger weapon dice, thus disqualifying this use case from the Dual Wielder requirement (one-handed melee weapons).

The Conclusion

While you can use a thrown handaxe and then attack with the longsword, you can only do so using the one-handed dice the Versatile weapon tag provides.