I think people miss the forest for the trees concerning trans people in history. They lived in an alien cultural with an alien mindset and you can see a lot of evolution and conceptual tinkering with the idea even just in the last seventy years to the point where people get really dramatically upset if you use the spelling of "trans[gender]" that was standard until just recently, so like, saying whether or not someone fully fits our idea of a trans person is very difficult. Things like the fact that living as a man did provide a lot of freedom a cis woman would not otherwise have had* and "this pervert loved pervert sex so much he wanted someone to give him a vagina" being exactly the kinna libelous screed people threw around do further muddy the waters to an extent.
However, none of that really matters. The result, such as with Dr. James Barry, is often so identical to being trans that it's ridiculous to call it anything else. It's very much possible he might not have been a man if cis women were able to do more in society during his lifetime, but as I've said before a trans man who comes to identify as a man as a result of experiencing misgoyny is even today still valid, and no matter what exactly was going on inside Barry's head, he lived the life he wanted to live. You would have to make the completely baseless speculation that he was totally miserable about the situation behind closed doors to say otherwise, but no evidence suggests anything of the kind.
In cases like Eleanor Ryker, it's like, people question if she was either a trans woman or just a crossdresser who roleplayed being a woman in her capacity as a sex worker, but I would argue that going off the very limited data we have she was not necessarily a "trans woman" by the 21st century Western definition but not merely a man who wore women's clothes either, something entirely different, a cross-cultural equivalent similar to kathoey or 2S folk.
*although it ofc came with risk of discovery, the closet is not a privilege
