It's not so much that gender is a series of social stereotypes. It's that those stereotype can help the individual and outsiders view themselves as their identified gender. Certain clothes can also give you the shape of your true gender identity. It is also a signal to outsiders of what pronouns you use so you don't get misidentified. A lot of trans people just want to be accepted as their gender and physical appearance is a major part of that. Especially at the start of transitioning a lot of people lean in to it extremely hard, and as they get further along they might ease up on the traditional gender roles.

I know personally I have one friend who is a trans woman and she is not feminine at all. And because of that people are constantly misgendering her, which she has expressed hurts her, but she knows it's usually not intentional. I don't think she is interested in being more feminine presenting besides have sex reassignment surgery to alleviate dysphoria she feels internally.

I wish I could find the comic now, but I also read something a long while back from a trans man. He talked about how he loved the color pink, and how he missed wearing pretty dresses from his days where he was seen as female. But he had to give it all up because it was too painful to be misgendered constantly.