Yes, your federal withholding is based on how your W-4 was completed. When you have a part-time job, it's common to have little or no federal tax withheld because the amount per pay period is low.
The income from your part-time job will be included with your other income, so it's possible that this W-2 will reduce your refund, or increase your tax due, but the only way to be certain is to do your tax return and see how it comes out.
If you want to make sure you have federal taxes withheld in the future, you can file a new W-4 form with your employer. Find guidance for this form at the IRS website.
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