"Gender Identity is the individual accepting a premise like: if females tend to be (nurturing, empathetic, gentle, supportive, and creative), and I feel (nurturing, empathetic, gentle, supportive, and creative), then I am a female."

I am not sure what kind of "gender theory" you are referring to, but this is clearly not what scholars teaching gender theory at universities say, it is not what natural scientist believe and it is definitely not what most transgender activist say.

Gender identity does not equal gender expression, gender roles or gender stereotypes. As you so correctly point out in the first part of the article, male and females overlap along all these axes, so gender identity cannot be reduced to one such trait or ability.

Are there trans people who point to stereotypical traits when they try to explain their transgender identity?

I guess there are, as this may seem like the easiest way to convey that they truly are who they say they are to cis (non-transgender) people. Many cis women also desperately try to live up to the stereotypes to be accepted as "good women", so it should come as no surprise that some trans women do so too.

But none of the major trans activists I know of believe in such a simplistic tale.

Trans people are like cis people when it comes to personality traits and gender expressions: They are all over the map. I know trans women who call themselves tomboys and there are, indeed, "femme" trans men around.

Gender identity (as opposed to gender as a social phenomenon) refers to someone's experience of being a man or a woman or non-binary. Gender identity refers to your sense of self. Nothing more. Nothing less.

If you want to write about gender theory, I suggest you read up on it first.