I don't think you can change this after the fact, but I recommend you talk to your state's Labor Department or Attorney's General office. They can tell you next steps.
Basically, your employer paid you as if you were an independent contractor instead of withholding (and paying) some of your Social Security taxes. As it stands now, with your 1099-NEC you will need to file your taxes as self-employed. This might help explain:
https://turbotax.intuit.com/tax-tips/irs-tax-forms/what-is-form-1099-nec/L5fbwIFSn
Good Luck!
