Is swearing falsely in national service termination procedures considered an oath that draws one into sin (yamin ghamus), and does that affect the validity of future earnings and livelihood?

You must offer sincere repentance for the false oath, as there is no expiation for it except repentance, according to the majority of scholars. As for your future work and earnings, there is no harm in them, and it is not necessarily the case that the oath will affect your sustenance. We hope that its ill omen will not affect your sustenance if your repentance to Allah is sincere.