My understanding is by medical standards, the evidence is pretty low quality,

Your understanding is wrong and influenced by transphobic rhetoric, not “medical standards”, which have considered puberty blockers safe and effective since at least the 1980s.

The use of puberty blockers is supported by twelve major American medical associations, including the American Medical Association,[14] the American Psychological Association,[15] and the American Academy of Pediatrics.[16] the American Academy of Child and Adolescent Psychiatry,[17] the Pediatric Endocrine Society,[18] the American College of Obstetricians and Gynecologists,[19] the American Association of Clinical Endocrinologists,[20] and the American College of Physicians.[21] In Australia four medical organizations support them,[22] as does the Endocrine Society,[23] and the World Professional Association for Transgender Health (WPATH).[24]

Overall, puberty blockers have demonstrated an excellent safety and efficacy profile in the treatment of precocious puberty. The most common side effects reported include nonspecific headaches, hot flashes, and implant-related skin reactions.[39]