What dates count for refinancing a home for a tax year?

The refinance in 2022 and the associated Form 1098 from your lender can only be entered on the 2022 tax return, next year.

You cannot put 2022 information on a 2021 tax return.   Wait until next year when you file  2022 return.

What do you think is deductible anyway?

You deduct interest when you pay it, you didn't pay interest on the new loan in 2021.  You deduct property taxes when they are paid the government, so any amounts you put in escrow are never separately deductible, only when the government is paid (and you will get a refund of any leftover funds from the escrow account at the first lender.)

The only thing that would be specially deductible from a refinance is:

a. if you paid points on the mortgage from the first lender,

b. and you are deducting those points spread out over the life of the loan instead of a lump sum in the year you bought the home,

then you can deduct the remaining points in the year the loan is paid off and refinanced, but only if you refinance with a different lender.  And that happened in 2022.