The Federal grant is taxable, so it is normal that by entering the form 1099-NEC, your refund decreases. $600 of taxes for a grant of $5,000 means that you are in the 12% tax bracket.
You are correct in answering that this grant is not money earned as employee or self-employed individual. By doing this, you are not subject to self-employment tax.
As you have already reported the grant on form 1099-NEC, do not enter it again in form 1098-T. You would be counting this income twice.
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