Custom entity equipment cannot be placed in the saddle slot

Relates to MC-80243 and MC-277526.

The bug

1.21.2 has introduced a more data-driven approach for entity equipment items. However, saddles, for some reason, remain hardcoded, and it's impossible to create another item which can be placed into the saddle slot via components.

How to reproduce

1. /give @s minecraft:green_carpet[equippable={slot:"body",model:"minecraft:blue_carpet"}]

2. /give @s minecraft:green_carpet[equippable={slot:"saddle",model:"minecraft:blue_carpet"}]

Expected results

Both commands would work; the first would give a carpet that can be placed in a body slot, and the second one that can be placed in the saddle slot.

Actual results

The first command works as expected, but the second command fails.