See this IRS FAQ:
"We" don't have a 401(k). A 401(k) is an individual account belonging to one person. Generally, if the person is still employed by the original plan sponsor (employer), no withdrawals are permitted unless the employer has a policy allowing hardship withdrawals. Meeting those rules is separate from anything COVID-related.
Then, if the person is no longer employed by the 401(k) sponsor, or the sponsor allows hardship withdrawals, the withdrawal can be exempt from the penalty if it is made between March 22 and December 31, 2020, AND the person making the withdrawal can certify one of the COVID-related situations described in the IRS FAQ. You will certify this on your tax return. You don't send proof to the IRS with your tax return, but keep the proof for at least 3 years after you file in case of audit.
Withdrawals from a pre-tax (traditional, not Roth) 401(k) are always subject to regular income tax. For Covid-related withdrawals, you can spread the taxable income out over 3 years or report it all at once.
Whether the PT job offsets your business losses is up to you to determine, you have to certify one of the hardship conditions in the FAQ.