It's relevant to the entire issue but not to whether, as you said, "...there were studies before, and more studies now which detail the over-reporting of trans incidence, the still furious debate over whether it's a genuine condition or a mental issue".

Keep in mind that the context was gender recognition certificates, which are primarily an adult thing (though in Scotland the age was lowered to 16).

You can't point to a pond full of geese and say, "Swans aren't real." All you can say is that these aren't swans. If someone else is calling them swans, you can correct them. If people are saying, about some other pond, "You can't go near the water! It's full of swans, and swans are dangerous!" you need to look at that water and see if those are actually swans, or whether people are mislabeling ducks and geese again. (You also need to understand whether they might be exaggerating the danger of swans.) But some swans still exist. Just because it might be convenient for you if they didn't--then you wouldn't have to check the water, and you could dismiss all the duck-and-geese-mislabelers without a second thought--doesn't mean that it's true.

If the question is whether every instance of reluctance to embrace gender norms means that someone is trans, then stuff like this is absolutely key evidence.

But with what you actually said, this is is only relevant in that the article you linked in the other reply not-very-cleanly supports the idea that you mischaracterized the situation before: it agrees that there is a real condition while making the case that there's the risk of a lot of false positive diagnosis in adolescents.