Should the upper floor of the mosque be closed until the first floor is full, while some worshippers are forced to pray in the mosque's outer courtyard, exposing them to heat and cold, or should it be opened to relieve them, even if it goes against the Sunnah of completing the rows?

Completing the rows on the first floor is in accordance with the Sunnah and is better than praying on the second floor if there is space on the first. Praying outside the mosque when there is space inside it is contrary to the Sunnah. The Imam should follow what is most beneficial, so he should open the second floor immediately upon the first one filling up; combining the Sunnah of completing the rows with concern for the comfort of the worshippers. If that is not possible, he should open the upper floor even if the lower floor is not full, prioritizing the safety of the worshippers.