Which is more deserving of prayer: the جامع mosque whose imams commit Bidʻah (innovations), or the prayer room in student housing which is free of such innovations, knowing that there is a fatwa stating that praying in prayer rooms is not considered congregational prayer and that the mosque is more deserving?

Congregational prayer in the mosque is obligatory upon able-bodied men if they hear the call, and what is meant by hearing the call is hearing the adhan (definition) with the usual voice without a loudspeaker. So, if you do not hear the call, it is permissible for you to pray in the prayer room of the residence. One should compare the benefits and interests to choose what is best.