Do I need to pay taxes on a 401K withdrawal, if I am 59 years 2 months and 7 days old and used the money to closing costs on a new home purchase?

it depends on your 401(k) plan.  You may not pay taxes on the amount if there is a repayment plan in place. If you did not receive a 1099-R for 2023, then you will not report it for now.

There is a difference between a loan and a withdrawal.  Loans are not taxable as long as you pay them back.

For a withdrawal, a 401k withdrawal is always taxable income, because you did not pay taxes on the original investment.  You will be subject to an additional 10% penalty for early withdrawal if you are under 59-1/2 on the date of the withdrawal, unless you were 55 or older when you separated from service with this employer.  A home purchase is not an exception to the early withdrawal penalty for 401(k)s.  It is an exception for IRAs, but IRAs and 401(k)s are different plans covered by different laws and regulations, even though they have a similar purpose.