Hi, Petunia. I'm sorry your wife didn't take it more positively, but - like others here - I think many of the things she did say give reasons to be hopeful. I think you're wise to move slowly from here. This was, as you wrote, only the start of the conversation; there will be more.
You said your therapist would provide a "supporting letter." Is that a Gender Dysphoria diagnosis? If so, that sounds like a pretty big deal to me. If your therapist is saying you are gender dysphoric, then I think that's something your wife ought to know about and really, truly understand its significance.
I'm very much an outsider, but from what I'm hearing your wife loves you and wants you to stay together AND she doesn't know about the profound significance that your being transgender has on you, your well-being, and therefore your relationship with her. Marriages are very much about openness and communication; this is something she *really* needs to understand.
But take your time, feel your way through. It's very new to her, and she will definitely go through her own transition as she adjusts to the new reality of you and the two of you. I find myself feeling pretty optimistic, though.