Is it permissible to make up the Sunnah (supererogatory prayer) before Fajr after the obligatory prayer, or is that an innovation?

What you did by performing the obligatory prayer and omitting the supererogatory one, if it was due to fear of the time expiring, then it is correct; because if the time becomes constrained, one must prioritize the obligatory prayer. However, if there was ample time, it would have been better to start with the supererogatory prayer. There is no sin in omitting it, especially if you feared missing a need or benefit. If you did not pray it at its time, then it is permissible to make it up.