Summary:
If you allow the soul speed enchantment to function in the armor.body slot and equip a horse with horse armor with that enchantment, the enchantment increases the speed on soul sand and soul soil as expected, however if you control the horse, it does not emit the minecraft:soul particles. To control the horse, you have to ride it while it is equipped with a saddle. Relates to MC-268936.

Steps to reproduce:

1. Install the attached datapack Soul_speed_on_horse_armor.zip.

2. /fill ~ ~ ~ ~20 ~ ~20 minecraft:soul_sand

3. /summon horse ~ ~ ~ {Tame:1b,body_armor_item:{id:"minecraft:diamond_horse_armor",count:1,components:{"minecraft:enchantments":{levels:{"minecraft:soul_speed":20}}}},SaddleItem:{id:"minecraft:saddle",Count:1b}}

4. Lure the horse around by holding a golden apple, golden carrot or an enchanted golden apple.
5. Notice that it emits soul particles as expected.
6. Ride the horse.
7. Move the horse on the soul sand.
8. Un equip the saddle.

9. /execute on vehicle run damage @s 1 minecraft:player_attack by @p

Observed result:
If the horse moves itself, it emits the particles as expected but if a player controls it by riding it when it is saddled, no soul particles are emitted.

Expected result:
Even if the horse is controlled, the soul particles should be emitted.

Video:
Minecraft 24w19b_soul speed.mp4