For a hardship withdrawal the first $1,000 is exempt from the 10% early withdrawal penalty. All of the amount over the first $1,000 is subject to the 10% early withdrawal penalty if you were under age 59 1/2 at the time of the withdrawal or you were under the age of 55 and have separated from the company that provided the 401(k).
There is not an exception to the underpayment penalty for hardship withdraws in general. However, for 2024, there is a $1,000 Emergency personal expenses distribution that can be exempt from the early distribution penalty. With a 401k, there is not an exception for education.
Any withdrawals you made in 2023 would need to be reported on your 2023 return. Those would not be eligible for the $1,000 emergency personal expenses. And in 2024, the withdrawals you made, should be included on your 2024 return.
Retirement topics - Exceptions to tax on early distributions