Is it permissible to perform the Sunnah prayers after the obligatory prayers, which one vows to perform in congregation, or must one perform the Sunnah prayers first and then join the congregation?

If you vowed an act of worship, you must fulfill it. If time becomes constrained for performing the vowed Sunnah due to the establishment of the obligatory prayer, then prioritize the obligatory prayer, for the Prophet, peace and blessings be upon him, said: "When the prayer is established, there is no prayer except the prescribed one." Then you perform the missed part of the vowed Sunnah after the prayer, even if it is during a prohibited time for prayer.