This happened to me twice in the past month. Am currently suitcaseless in Tokyo.

They've said they will compensate any reasonable emergency expenses (clothes and toiletries). As a back up, check your travel insurance or the credit card company you booked your ticket/hotel with.

My card company will compensate up to $1000 for a baggage delay if the airline doesn't pay up.

Get what you need today and assume you'll have your suitcase tomorrow. If it doesn't arrive then continue shopping and keep all receipts.