I'm told that paramedics, when transporting an unconscious person, ask family/friends if they have any mental illnesses.
Does gender dysphoria qualify?
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as you noted in comments about England context:
After a detailed assessment to confirm the diagnosis of gender dysphoria and what it means for you, the GDC team will work with you on an agreed treatment plan.
Before that, it's just feeling or symptom from medical point of view.
Same reference from NHS states:
Gender dysphoria is not a mental illness, but some people may develop mental health problems because of gender dysphoria.