@rmcafe22 if you are US person ( citizen/Green Card ), you are required to file a US return covering your world income. A US entity issuing a 1099-NEC to a foreign worker is not correct really but would be correct for issuing to a US person -- the issue here is that you a US person earned this income as a foreign person ( worked while stationed abroad). Thus the quandary --- to you this is foreign income because it was earned abroad, tax home foreign.
1099-NEC is reported using Schedule-C whether you are a self-employed/ a contractor/ sole proprietor etc. -- it is not specific to business -- just where you work independently and not for a employer ( whether US based or not ).
For your ref: ----> https://www.irs.gov/pub/irs-pdf/i1040sc.pdf
See page C-5 ..Line 1.
I hope this satisfies your doubts about using Schedule-C to report 1099-NEC income
