"Eonism" was a term invented by Havelock Ellis in the 1920s, because he thought Magnus Hirschfeld's use of the term "transvestism" did not adequately convey a meaning of cross-dressing without an obvious sexual motive. He discusses this in the first part of
Studies in the psychology of sex. Vol. VII, which you can read online for yourself.
Hart is starting to get to the period of time, from roughly the 1920s or 1930s, where modern transsexualism begins, so it's possible that Hart would have — if asked in today's terms — consided herself "transgender". But the evidence does not support much more than Hart being a butch lesbian, as you'll see if you read the post I quoted earlier. As for "medical transition", Hart had a hysterectomy because she did not want to become pregnant. Some articles (from the past 10 years or so) claim that Hart took testosterone to appear more masculine, but without citing any sources. (Testosterone was approved in the US for medical use in 1939, and Hart died in 1962 aged 71, so it's possible but, again, no proof.)
If you come to the thread and want to claim a historical figure was "transgender" as we now understand the term, you should come with more than just an assertion.