To clarify, are you sure the form is not Form 1099-MISC rather than Form 1099-NEC?
Form 1099-NEC is ONLY for Self-Employment income.
Yes, you are correct in that you cannot enter this in the entry for 1099-NEC or else this will be taxed as self-employment income.
Here's how you should enter this so it shows up in your tax return as "other income", in TurboTax Online:
1. Navigate to Federal > Wages & Income> Miscellaneous Income, 1099-A, 1099-C > Add/Edit
2. Choose Other reportable income
3. Enter a description such as "Connecticut Hero Pay" and the amount
Per IRS Guidance from Senior Stakeholder Liaison Joseph McCarthy, "In the event that an IRS notice is issued by the IRS due to self-employment tax not being reported on a tax return the recipient should respond to the notice explaining that the 1099 NEC is for CT Premium Pay Program (Hero) payments and is not self-employment income."
See also: Important New Tax Guidance from DRS, IRS on Connecticut Hero Payments