Quite extensive research actually. The overwhelming medical consensus is that puberty blockers are safe, and this is backed up by over three decades of their use in treating trans youth and even longer in treating precocious puberty.

I leave it to the reader to determine whether they think having to take vitamin supplement counts as a significant side-effects. I would note, however, that it is also important to put these side effects in context. The contraceptive pill, for instance, also has reduced bone density as a possible side-effect.

My reading of the research also does not indicate that it is majorly lacking. Medical research is written in a very conservative manner. Researchers avoid making claims beyond the limits of their research. This can look like doubt or uncertainty when it is not.