Is the custom of giving the wife gifts on the Day of Aashura within the scope of the Hadith which encourages some lavishness on this Day?

Answer

It is not within the scope of the Hadith. Aashura is not like Christmas day is for Christians. They exchange gifts on their Christmas day. The Hadith pertains to increasing on food to be consumed, not on gifts. The custom of gifts is in emulation of the kuffaar. It is a new-fangled bid'ah. The Sahaabah did not exchange gifts or give gifts to their wives on this Day.