Is it permissible for travelers temporarily residing outside their city to pray jamaʿah (in congregation) and qaṣr (shortened) in their private accommodation, given that they sometimes do not pray in the mosque?

As long as you are not staying in Jeddah for the period that breaks the journey, you are considered travelers and are entitled to the concessions of travel, such as shortening and combining prayers. As long as you pray in congregation in your accommodation, we hope there is no blame upon you for not going to the mosque, because the obligation is fulfilled by performing it in congregation, even if not in a mosque. Prioritizing the attainment of the virtue of congregational prayer over shortening it is what is held as the ruling by us.