Yes, agreed, that's largely true.

I don't think we're anywhere near done, even in that case, though.

There are still mental health issues co-occurring, and those are only reduced, not eliminated, by living in the most supportive environments. There seem to be long-term risks for some medical conditions (e.g. heart disease or stroke). People report a wide range of psychological impacts of hormone therapy, and we don't have much ability to predict who is at risk, or always have good alternatives to offer for those who find it difficult to tolerate the most common treatments. (The situation for testosterone blockers is pretty good, though, I think.) And so on.

The issue of having children is an especially complicated one. If one is trans and doesn't want children, no problem! But many trans people do want children (of their own), which raises a whole host of difficult questions about the age at which the (known) solutions should be applied, especially given that non-trans people often change their minds about children (though not so much after 20s if they were really clear on "no" before). Puberty blockers let you delay the decision, but the reproductive and secondary effects of puberty are not separable (up to the point where one could at least isolate viable gametes).

But beyond the clearest cases, there often aren't any results at all, let alone well-established solutions. People say "conversion therapy doesn't work" on the one hand but "if you feel distress about your gender, talk to a psychologist" on the other. That can't both be right unless there's a strong cis / trans dichotomy! Either psychological help is uniformly useless when anything has to do with gender identity discomfort; or there are a set of people for whom therapy is an alternative to nothing-or-transition; or transness can only be binary. You seem to adopt the latter view with your language: "rather than actually being so"; "if they are in fact transgender". But I don't think that's established.

What is established is that there are definitely trans people with a (reasonably) clear presentation and that there are cultural, hormonal, and surgical solutions for them that are a marked improvement over nothing. I'm not sure it matters how the neural basis turns out--if someone has a "female" brain, to the extent that there is such a thing, in a female body, but that female brain for whatever reason has a male-body-and-man-gender-self-image (but everything else about the brain is female), are we really going to withhold the usual treatment from them? I would hope not!--unless it turned out that in such cases, standard gender affirming care was not a solution.