Horses no longer drop their horse armor when the gamerule doMobLoot is false

Summary:
As of snapshot 24w05a horses no longer drop their horse armor if the gamerule doMobLoot is set to false. This is due to the change how horse armor is stored. They still drop their saddle though. Relates to MC-15114.

Steps to reproduce:

1. /gamerule doMobLoot false

2. /summon horse ~ ~ ~ {Health:1f,Tame:1b,body_armor_item:{id:"minecraft:diamond_horse_armor",count:1},SaddleItem:{id:"minecraft:saddle",Count:1b}}

3. Kill the horse.

Observed result:
The horse only drops its saddle, not its horse armor.

Expected result:
The horse should drop its horse armor too just like before 24w05a.

Video:
horse doMobLoot false 24w04a.mp4
horse doMobLoot false 1.20.6.mp4