Actually 'dysphoria' just refers to a strong negative emotional state of unhappiness and frustration, which is common to multiple disorders.
'Gender dysphoria' can involve intense disgust at one's sexual characteristics, although 'anatomical dysphoria' is not a requirement for diagnosis (for example, for children six characteristics from a checklist of eight are required, and only two on the list refer to dissatisfaction with anatomy).
However, if people want to change characteristics of their sex, this is more appropriately described as sex dysphoria since it is their sex they are unhappy with, not their 'gender'. If somebody simply doesn't 'identify with their assigned gender', where gender is defined as a set of socially-constructed expectations, then this is just a fancy way of saying that somebody is gender non-conforming. Saying that somebody needs to change their sex characteristics as a result of being gender non-conforming makes no sense. Nor does describing attempts to help somebody feel more comfortable with their biological sex as 'conversion therapy' for gender identity make sense if sex and gender are separate.
Here is a
description of experiencing 'gender dysphoria' from a detransitioner.