Bracers of Archery is a magic Bracers in Pathfinder: Kingmaker.
It might not be clear from description, but you get proficient with longbows and shortbows while wearing those bracers.
The Attack bonus is of [Other] type, not [Competence]. The Damage bonus is [Competence] as intended. (Last Version:2.1.7b) (Kingmaker)
The Attack bonus is of [Competence] as intended. The Damage bonus is [Competence], but seems to invisibly stack with other competence bonuses. (Last Version:2.1.3j) (Wrath of the Righteous)