I have only been on HRT one year and definitely not taller now. Actually my height dropped far too much prior to HRT.
In my 20s I was 5'11" (180cm). I hadn't bothered to measure for many years, always filled in forms that way. I started seriously considering transition at age 53, measured my height and realized I was 5'7" (170cm). That was quite a shock... I had not been to a doctor in more than a decade. I immediately started looking for a GP and an endocrinologist, ordered blood tests and began the medical process of transition. My endocrinologist ordered a bone density test to set a baseline, I'll re-measure that in the next year or two. My only chronic health issue had been occasional back pain and that has now stopped.
I wasn't surprised to confirm my natural hormone levels were off. I had a choice: take testosterone or estradiol. Easy decision.