I believe that transsexuals have a mental health condition called gender dysphoria which causes them great distress.
As for the term trans which you have used in your OP, according to Stonewall the term trans includes "transgender, transsexual, gender-queer (GQ), gender-fluid, non-binary, gender-variant, crossdresser, genderless, agender, nongender, third gender, two-spirit, bi-gender, trans man, trans woman,trans masculine, trans feminine and neutrois" and is an "umbrella term to describe people whose gender is not the same as, or does not sit comfortably with, the sex they were assigned at birth"
So I suppose I agree with you, that trans is not a mental health condition, as many people will fall under that brolly, including myself.