You would still have the same age, gender, personality, skin color, etc. and you would be able to speak at least one local language and would know basic information of the era and place. Your family, social standing, and such would be randomly picked.
The surgery that kept me alive at birth wasn’t invented until the late '80s. So I guess I would just be fucked no matter what. So put me wherever they want, any time before 1950 is going to suck ass for me.
Now assuming that part of my time travel comes with being able to fix my heart stuff. I would like to be born in the early 1900s. I can’t think of a single time where I’m not going to fight both war and awfulness in the general world. But at least then I could be around for some cool developments.
You’ll be right - OP said your age and a bunch of other things would be preserved. You won’t be born there - just transported to the chosen time, to spend the rest of your days.