Well, in general falsifiability and its application to psychology is up for debate because it is generally unethical/impossible to run single variable control experiments on humans :)

https://www.frontiersin.org/articles/10.3389/fpsyg.2015.0062...

You don't need to have single variable control to make inferences about differences between population subgroups, only to infer causality.

We certainly know that people who identify as transgender are at higher risk of suicide than the broader population.

Exactly, I was poking at the confidence expressed by the OP that inferred causality. Having more nuance and expressing less confidence would be closer to reality.

Irrelevant in this case. You don't need a double-blind experiment to determine suicide rates, as I already said.