Alternatively: gender and sex could be synonyms, and trans people experience dysphoria because of a mismatch between physical gender/sex and their self-perceived gender/sex, through a mechanism not all that different from other kinds of dysphoria.

BTW, I am physically male, but don’t perceive or think of myself as of any sex or gender (I think the word is “genderless”), so might as well say I have the “gender” of an inanimate object.