Will the female physical therapist bear a burden and responsibility before God for falling short in the patient's right as a result of her superior delegating some session tasks to nurses, and is her salary permissible?

Your salary is lawful as long as you perform your work as required. Your boss's negligence towards patients does not affect the lawfulness of your salary, nor does it burden you with sin, as long as you have condemned this negligence and advised him to assign treatment to specialists. If he does not respond, then escalate the matter to the authorities.