The only possible deductions you have on your new primary residence purchase for 2022 is property taxes and mortgage interest, which most likely would have been paid that the closing. That's pretty much it. Since those are SCH A itemized deductions, chances are it would make no difference on your 2022 tax liability anyway, as SCH A deductions do nothing for you on the tax front, until the total of all of those itemized deductions exceeds your standard deduction.
now wondering if I can legally claim the closing on my 2023 taxes.
No. any deductible expenses incurred/paid in 2022, would have to be claimed on your 2022 tax return. You can't change that.
