I would expect it to be in melee mode.
What I am seeing is that the Combination firearm weapon trait already lets you make a Ranged Strike with the weapon while it is in melee mode. But it is a second action, has to be immediately after the Melee Strike, and MAP applies normally.
Triggerbrand Salvo narratively does the same thing. You make a Melee Strike, then a Ranged Strike with the Combination firearm weapon. But in this case it is one action for both, MAP doesn't increase until after the Ranged Strike, and you get a +2 bonus instead of the MAP penalty.
But with the two being so close narratively, I would have the firearm in melee mode when done, same as with the Combination trait ability alone.
Besides, since the weapon is now empty, that is probably the mode you would rather it be in anyway.