Great job, Mama Bear! And you've given invaluable advice here, too. I think many parents of trans kids underestimate the need for a therapist in general, let alone, one that specializes in gender. Some people say their kids are confident and "don't need" a therapist, or they don't want to "stigmatize" being trans (or make it seem like something that needs clinical care). But, as you've pointed out, when a trans child grows older and desires any number of available trans medical or surgical interventions, including something as simple as puberty blockers, you can't just walk in and ask for them.
For our family, at least, that was the experience. Just blockers required the process of our child seeing a therapist who specialized in gender (and seeing her for several years to establish a documented pattern of gender dysphoria), and the dysphoria required a clinical diagnosis. All of that had to be in place before we could even see an endocrinologist for the first consult, and we had to have a referral to them from our gender therapist.
So, it's not just beneficial for our trans teen's mental health; it's necessary for trans medical care (and insurance coverage) as well.