Given that many nations are indeed going forward with such legislation, have we actually observed a decrease in the number of trans people attempting suicide or self-harm?
I suspect that because a) most countries are still too low in the foothills of real reform, and b) most of that lower-level reform has in any case only been introduced very recently, it is currently too soon to be able to gather robust/credible data on this.
However (as I've said before), I think it's absolutely feasible to look to the introduction of legislation around gay rights as a suitable proxy, coupled with the clear historic (to the present day) high incidence of suicide/attempted suicide amongst transgender people (especially when linked with the stated underlying reasoning).
So... what we have is a current situation where the apparent incidence of suicidal intent among transgender people is shockingly high, when compared with any other demographic group. And we also have decent evidence that this high incidence is primarity due to abuse, marginalisation, non-acceptance, bullying, lack of (and denial of) rights, and so on.
And from this - and looking at the gay rights comparator for further guidance - I believe it's fair to form a credible hypothesis that the incidence of suicidal intent among transgender people is very likely to fall significantly as and when transgender identity rights are properly recognised and protected (as was the case for gay rights between around the 1960s and the 1990s).
But we will only be able to get the direct evidence to evaluate in, I would suggest, at least 5 years from now. In the meantime, I propose that the above hypothesis is a reasonable kicking-off point.