I entered the amount of my 2023 Federal Refund into my income for 2024, left, and when I came back and logged back in, it was missing! Where is it?

The tax year being filed during calendar year 2024 is for tax year 2023.  The 2024 tax year will not complete until after 12/31/2024.

You do not enter a federal tax refund on a federal tax return.

Not quite sure what you are trying to do.   No one has prepared or filed a 2024 tax return.  That will happen next year in 2025 when tax year 2024 is over.    People are currently working on preparing and filing tax returns for tax year 2023, the tax year that just ended on December 31, 2023.

You do not enter a federal refund you received anywhere on a federal tax return.  It is not taxable.  There is no place to enter it.   

Are you working on a state return in which you are being asked for last year's federal refund?  There are a few states    (Alabama, Iowa. Missouri, Montana, and Oregon) 

 that want that information----but if you are working on a 2023 tax return, it is asking you for a 2022 federal refund.