Wolf armor loses custom display name and other NBT when equipped

The bug

When a wolf equips armor that has custom NBT data that data is lost. For example if you rename wolf armor using an anvil the item will lose its name when the armor is removed. This is inconsistent with other mobs like zombies that preserve the NBT of items they pickup and equip.

How to reproduce

1. Spawn a tamed wolf:

   /execute summon wolf run data modify entity @s Owner set from entity @p UUID

2. Give yourself a renamed wolf armor item:

   /give @s wolf_armor{display:{Name:'"Test"'}}

3. Equip the wolf armor on the wolf

4. Use shears on the wolf
   → ✔ The wolf armor is dropped
   → ❌ The wolf armor has lost its custom name