Should a therapist continue treating a patient, and then the next patient, which leads to missing the Dhuhr and Asr prayers, knowing that delaying the treatment will cause severe harm to these patients?

It is incumbent upon a Muslim to fear Allah and to know that delaying prayer beyond its prescribed time is a grave sin, indeed considered disbelief by many scholars. What has been mentioned is not an excuse that permits abandoning prayer or delaying it beyond its time; rather, it is closer to mockery. A person must safeguard their prayers. Ruqyah (definition) and adhkar are aids used for treatment, but it is not permissible for them to distract one from the obligatory prayer. Rather, performing prayer is one of the most important means of healing. If a sick person would be harmed by abandoning treatment, then it is permissible for the physician to combine two prayers according to those who permit combining prayers out of necessity. What has been mentioned does not justify abandoning prayer or delaying it beyond its time, and whoever does so exposes themselves to Allah's wrath and punishment.