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
In version 1.21.10, I was able to successfully have husks summon reinforcements in the end dimension. For the nether, I think this might be intentional, as the nether doesn’t have access to the sky light, even above the nether roof and I think the way husk spawning works is that it can only succeed if it can find a block with sky level of 15 which it can’t.
My test video: https://www.youtube.com/watch?v=SwHMHcpCkPs