What worries me more about the accuracy or inaccuracy of the stats, is how the stats are used.
When it is used "41% of trans people attempt suicide" it is always followed by So....
"Give us everything we want, full validation, access to anything we want, or we are all going to die"
Even more mildly "So listen to what we want and give it to us"
What it looks like under a different analysis is that Transgender ideology is a magnet for troubled teens or people with other underlying mental health issues.
It attracts the same demographic as teens who would have suffered from body dismorphia. Believing your fat when you aren't. Turning to anorexia or bulimia or use of steroids to look muscly.
Psychiatrists frequently identify underlying causes in body dismorphia. A lack of self esteem. A need to be in control of what people think about you, a need to assert control on your world when you feel entirely powerless, a need for validation, to hear people talking about you the right way. In extremes it leads to total change of physical appearance. Transgenderism is not much different to other disphorias that lead to anorexia/bulimia.
One in five anorexia deaths are from suicide.
There is a high rate of suicide in those on the autism spectrum. A study in 2016 concluded that suicide was the leading cause of premature death in people with ASD. There is a correlation between ASD and Transgenderism.
Transgenderism offers many solutions to the troubled person.
An alter ego that will be praised and celebrated.
Control over people around you. You get to dictate use of pronouns, new name.
You receive a lot of special attention.
You feel celebrated and powerful and have a platform to express yourself and your world views.
You get a free pass to bully anyone who says anything factual.
There are certainly many factors that contribute to a high rate of suicide in trans people, if there is a higher rate amoungst them than other groups at all. But responding to it with total affirmation is doing far more harm than good.
(Including adult cross dressers in the transgender group makes any analysis rather more complicated because they are very contented).