The study you link cites a metaanalysis which found that "after sex reassignment, 80% of individuals with GID reported significant improvement in gender dysphoria . . . 78% reported significant improvement in psychological symptoms . . . 80% reported significant improvement in quality of life . . . and 72% reported significant improvement in sexual function" and concludes that "very low quality evidence suggests that sex reassignment that includes hormonal interventions in individuals with GID likely improves gender dysphoria, psychological functioning and comorbidities, sexual function and overall quality of life."

The data we have on the phenomenon is poor, and trans people suffer from comorbid mental illness at a vastly elevated rate relative to the general population, but the data we have does suggest that transition improves mental health and reduces the risk of suicide.

The study you linked does not address that, because the control is the general population. In fact, the study you linked specifically warns against using it the way you did:

"For the purpose of evaluating the safety of sex reassignment in terms of morbidity and mortality, however, it is reasonable to compare sex reassigned persons with matched population controls. The caveat with this design is that transsexual persons before sex reassignment might differ from healthy controls (although this bias can be statistically corrected for by adjusting for baseline differences). It is therefore important to note that the current study is only informative with respect to transsexuals persons health after sex reassignment; no inferences can be drawn as to the effectiveness of sex reassignment as a treatment for transsexualism. In other words, the results should not be interpreted such as sex reassignment per se increases morbidity and mortality. Things might have been even worse without sex reassignment. As an analogy, similar studies have found increased somatic morbidity, suicide rate, and overall mortality for patients treated for bipolar disorder and schizophrenia. This is important information, but it does not follow that mood stabilizing treatment or antipsychotic treatment is the culprit."