@BLR006 , since you entered the USA in 2014, your exempt ( from counting days present ) period ended in 2019 . Thus from Jan 1st 2020 your presence in the USA counted for purposes of Substantial Presence Test ( 183 days counting all days in current year, 1/3 the days present the year before and 1/6th the days present the year before that) and so you became Resident for Tax Purposes in the middle of 2020.
Many states have their own version of FICA and are actually exempt from collecting / contributing / participating in the FICA scheme and therefore I do not believe your old "practical training" employer would help with FICA -- also that implies that you as an employee of that state / local govt. entity is immune from participation of FICA. Please talk to your old employer to make sure that is the case.
Also note that being a resident for tax purposes has nothing to do with FICA -- it is question of whether you are participating in a required/optional training rather that being a professional employee.
In my view ( especially if the old employer was in a state that does not participate in the FICA scheme), it is better to leave things alone and proceed with the current employer / trainer on FICA. This is especially true , if you are not going to stay in the USA past your STEM-OPT period --- because the only gain is in Social Security credits and for this one or two years would not change anything.
Does this make sense or am I in the left field ?
Is there more I can do for you ?
Namaste ji
pk
