Even if you give husk sky access in the Nether or End dimensions it will not spawn reinforcements.

Test it with the zombie command and see it works.
Then test with the husk command and see it fails.

/summon minecraft:zombie ~ ~ ~ {attributes:[{id:"minecraft:spawn_reinforcements",base:1.0}]}
/summon minecraft:husk ~ ~ ~ {attributes:[{id:"minecraft:spawn_reinforcements",base:1.0}]}

Nether test video: https://youtu.be/0cSze7Bz9G4
End test video: https://youtu.be/oKyWoAPFar4