Is what was done—waiting for the procedures to finish in order to pray another congregational prayer after the first congregational prayer had passed—considered correct or incorrect, and does it entail sin?

If leaving the place does not entail significant harm, or if he can entrust it to someone, then it is more virtuous to pray with the first congregation. However, if leaving it would result in financial loss or hardship, then there is no blame in delaying as long as the time for the prayer has not expired, especially with the hope of finding another congregation, as the virtue of congregational prayer is achieved with any congregation. Among the excuses that permit absence from congregational prayer is fear for one's property.