Reimbursement for moving expenses is taxable income. However, if you are a W-2 employee, the stipend should have been included in your W-2 taxable wages, and be subject to income tax, social security tax, and medicare tax withholding. By putting it on a separate 1099-NEC, the employer is, intentionally or accidentally, making you pay both halves of social security and medicare (via 15% self-employment tax) instead of withholding 7.65% social security and medicare and paying the other 7.65% themselves.
You should first contact them and ask them to cancel the 1099-NEC and issue a corrected W-2. If they refuse, when you enter the 1099-NEC, there is a list of special circumstances and one of those is "this was paid to me by my employer and should have been included on my W-2." Turbotax will prepare a form 8919 with code H, and will add 7.65% social security and medicare tax to your return, instead of 15% self-employment tax.
You should not have a schedule C for self-employment and you can't deduct moving expenses against the income. You can still list moving expenses in Turbotax because they may be deductible in some states depending on your other tax information, but they are not deductible on your federal return.
