As of Minecraft snapshot 24w36a, horse armor has the minecraft:damage, minecraft:max_damage, and minecraft:repairable components despite not taking damage in vanilla or previously being repairable. This change was not mentioned in the changelog, leading me to believe it was made unintentionally.

As the minecraft:damage and minecraft:max_damage components are present, horse armor of the same type can be combined via crafting. This can be observed from the vanilla game without using commands.

The effects of damageability can also be seen by gliding with horse armor that has the minecraft:glider component, as the gliding enabled by this component will damage any damageable item. An example item that reproduces this behavior can be given by the following command:

/give @s minecraft:diamond_horse_armor[glider={},minecraft:equippable={slot:chest}]

This change also breaks commands modifying the stack size of horse armor, such as /give @s minecraft:diamond_horse_armor[minecraft:max_stack_size=99], as the minecraft:max_stack_size component conflicts with damageable items. This issue was discovered while testing MC-269637, which uses stackable horse armor as part of reproduction steps.