Profit of home sale split between two years

It depends.  The general rule for claiming income on a tax return is when you have constructive receipt of the money meaning you have an unrestricted right to it.  

In your situation the sale is not complete which would indicate you might have to relinquish at least part of it if the sale does not close. If this is the case, then you report the sale in 2023, because the actual close of the sale is in 2023.  You will have to determine that in your situation.

Reporting the sale:

The sale of this house would be reported on Schedule D as an investment sale if inherited and it was not your main home.  In other words you did not use this as your main home.

If this is considered investment property, report the sale using the steps below:

1. Under Wages & Income scroll to Investments & Savings
2. Select Start/Revisit beside Stocks, Cryptocurrency, Mutual Funds, Bonds, Other (1099-B)
3. Select Add Investments or continue to go through the screens to select 'Other' > Continue
4. Begin to enter the sale description >  Under Type select Other > Under How did you receive select 'I Inherited it' (if applicable)
5. For TurboTax Desktop you would enter the description 'Inherited Property' and select 'Long Term' as the hold period
6. Enter your sale date and 'Various' as the Acquired date
7. Continue to complete the screens until you arrive back at the Wages & Income main page.

Inherited property is always considered to have a long term holding period which provides favored tax treatment.

Cost basis for inherited property, if you were not a previous owner (name on property before the death of your parents), is the fair market value (FMV) on the date of death.  If the sale occurs relatively soon after the death of the owner then the FMV would be very close to the selling price as a rule. Check with the executor or a real estate company or the court records for other sales of similar property if necessary.