Is the questioner obligated to do anything regarding her not summoning the hospital's rapid response team for emergencies, despite the poor condition of some patients, which resulted in their transfer to the intensive care unit, and in one case, she does not know the fate of the patient?

The employee must fulfill their trust and perform the agreed-upon work, as Allah Almighty says: ﴿O YOU WHO HAVE BELIEVED, FULFILL [ALL] CONTRACTS.﴾ If it is not clear that the patient's death was due to negligence, then no expiation (kaffarah) or blood money (diyah) is required, because the basic principle is the acquittal of responsibility, and liability is not established by doubt. What is obligatory is to repent to Allah for the negligence.