The Gunslinger gains the Gunslinger Weapon Mastery feature at 5th level, which states: “You gain access to the critical specialization effects for firearms and crossbows.”
However, the melee part of a combination weapon has its own weapon group. For example, the melee part of a gun sword belongs to the Sword group, and the melee part of a hammer gun belongs to the Hammer group.
Does this mean that even though a Gunslinger can use the proficiency of the ranged part when making attacks with the melee part of a combination weapon (as described in Slinger's Precision), they still cannot apply the melee part’s critical specialization effect when they critically hit with a melee Strike?
That sounds right to me.
Many characters don't get critical specialization effects of the weapons that they use. That is a perk - not a baseline expectation.