I've been there and then some and did I ever worry! I was convinced they would never let me through the door let alone on T given my past MH history.
Then I discovered that many of us have a significant struggle with mental health before transitioning and they understand that being born in the 'wrong body' is a causal factor for these.
Additionally, atypical gender identity is frequently comorbid with many other neurological disorders including OCD.
I have a long patient file, hospitalisations, suicidal, been diagnosed with a range of personality disorders.
Today I'm Autistic, ADHD and trans.
After starting hormones my intrusive thoughts have gone way down and my mental health is far more stable, I'm more confident and comfortable in my skin.
I have a therapist and a psychiatrist and they manage my general mental health. It was enough for the gender doctors to know that my MH was well managed and that my therapist and psychiatrist approved the transition.
Knowing that my MH was well managed; the gender doctors viewed my previous mental history as evidence of my dysphoria in the past, and my current diagnosis of neurodevelopmental disorders further strengthened my case since they now know that there is an established connection between the two.
Don't be afraid of this, be honest and open about your past and how you are now handling it with your therapist and it should work in your favour.
Hope it goes well!