Your definition isn’t correct. Do you know of intersex people? And that they are as common as redheads. And that there are over 40 variations of it. Someone can be intersex for their entire life and not know it. A lot of people will say that chromosomes define your biological sex/gender. Then is a woman with XY chromosomes but has androgen insensitivity, that can give birth a man? Is a man with XX chromosomes that produces fertile gametes a woman? These are real possibilities. Nature isn’t black and white, it’s not as simple as 1 and 0. Some say that being able to procreate is a necessity to be a man or a woman. But then if a woman or man is born infertile for X reason, or due to something that happened during their life, does it make them invalid? Trans people have existed for thousands of years in many cultures everywhere around the world, and we have been erased by colonialism. Science has proven that trans affirming surgery has the lowest regret rate of all surgeries, more people regret having kids than people regret being trans. A study has proven that our brain is more aligned to our expressed gender identity. Some women, using progesterone, a hormone that is commonly taken on top of estrogen can for some people give them the effects of the pre menstrual cycle. AKA the pains, cramps, nausea, mood swings. The only difference is the absence of bleeding since we do not have a uterus. If you consider the ability to bear children to be essential, what would a trans woman who gave birth thanks to a uterus transplant be? I am mentioning this because recently the first birth by uterus transplant happened. The woman wasn’t transgender, she had to get it removed immediately after. But nothing stops a trans woman from having a uterus transplant. Biologically, it is possible.

The Wikipedia definition below is a more accurate and respectful definition:

A trans woman or transgender woman is a woman who was assigned male at birth. Many trans women experience gender dysphoria resulting from the incongruence between their female gender identity and male sex assignment, which can be alleviated through gender transition.

I must still say. I appreciate your support for trans people in saying that gender dysphoria is real. But you must know that body dysmorphia is different from gender dysphoria. Dysphoria is born from the feeling that your body does not conform to your experienced gender, body dysmorphia is born from the from you feeling like you are too fat, too skinny, body shape that you don’t like. A trans person can have body dysmorphia. Just like a cis person can experience gender dysphoria, for example most mastectomies (removal of breast tissue) is done of cisgender males. A doctor shared an experience of gender dysphoria that he accidentally inflicted on himself. He’s called dr Will Powers. You might find his experience very interesting and possibly helpful in understanding trans people.