Hair extensions are permissible and don’t affect ghusl or wudhu if the extension is placed at a length from the root (like 5 inches or more).
During ghusl, the hair doesn’t need to be washed. The skin has to be washed, and the part where the hair is attached to the skin. So it’s permissible to use extensions and the ghusl would be valid.
As for wudhu, one must either wipe the scalp or the hair if it’s not too long. It it’s like more than 5 inches long one must wipe the scalp. Now if the extension is placed at the hair less than 5 inches from the root, you would need to wipe the scalp even if the hair is not long.