I think it’s effectively impossible to remove societal influence from the equation - in other words, we can compare between different local environments and personal histories, but there’s no trans youth in the western world that hasn’t grown up in an at least moderately hostile and othering society.
I think you may be able to do some comparative analysis based on different rates of depression & suicidal ideation among homosexual youths both over time and across different states/local environments to get a sense of the magnitude of the social effect, but it’s basically impossible to fully disentangle social effects when evaluating the mental health of trans youth when you’ve got senators and governors proposing bills decrying them as ‘less-than’.
But, let’s try an experiment: let’s keep working on society until that’s _not_ the case, and if there’s still a substantially higher incidence of trans suicide in a world in which they’re supported and have care options available to them, I’ll owe you a coke.