Do I need to pay self-employment tax if converted to w2

I graduated college in May 2021 and started a job in June.  I was hired in a trial basis, with the intent to become a full-time employee.  My employer required that I submit weekly invoices for all of 2021 and I received a 1099-nec.  I became a full-time employee in for 2022 and received a W2 for that tax year.  I received an IRS notice CP200 stating I owe self-employment tax for the 2021 income.   Is this correct given that I was hired full time and am still employed at the same company?  The only difference was the submission of invoices.  I did not start a business.  Is it worth me pursuing an exception to paying the self-employment tax?