i tried looking it up in the datamine guides on discord (acnh info), and while i couldn't find an exact answer, on the chibisnorlax's guide they mention:
"I traded one of my first five villagers with a ‘basic’ house layout, will they have a proper/default layout on the new island?
Yes. Additionally, any furniture, fish/bug you gifted them and is on their floor will be reset when they move to a new island."
anecdotally, i have seen people say that the houses decorated using HHP reset after moving to another island! i don't have any expereince so i can't speak to how accurate or updated this info is but hope that helps a little