So long as you were actively trying to rent after the renter moved out, (i.e.; advertised as "for sale or rent" as an example) all costs incurred and paid in 2023 are deductible rental expenses on SCH E for 2023.
Date sold is the closing date of the sale. So you won't report the sale until next year when you complete your 2024 tax return. Any carrying costs will be claimed on the 2024 tax return next year, regardless of what year you actually incurred/paid those costs.
