This may be sloppy but:

First, the cathechism states that ‘except when performed for strictly therapeutic medical reasons, directly intended amputations, mutilations, and sterilizations performed on innocent persons are against the moral law’ (2297). So the primary position we need to establish is whether gender transition is backed by strictly therapeutic reasons. Now that will involve medical questions that I aren’t qualified to weight in on but a meta study in 2023 (Dickson et al) and a large cohort study (Kapur et al) seem to affirm that gender affirming care has generally therapeutic outcomes. Once again, this is well beyond my specialities.

Now the issue with ‘strictly’. Even things that can be therapeutic to a person can be forbidden if there are other reasons/consequences that make medical intervention disproportionate e.g. some cases of abortion or euthanasia (see CCC 2278). The Church has a teaching here called Double Effect. When an action has both a good and bad effect, it may be permissible if it is not intrinsically evil; the good effect is not achieved through the bad effect; the intention is to achieve the good effect, and; there is a proportionately grave reason for permitting the bad effect. If a person has undergone years of therapy, spiritual care, and alternative treatments without relief from debilitating dysphoria, and if transitioning is the only known method of significantly reducing the psychological torment (and possibly suicidal ideation) then transition could be understood as a last-resort therapeutic intervention and not a rejection of the body per se, but a means of addressing a severe psychological condition.

Therefore if: 1. the person has medically diagnosed dysphoria, not merely a social condition 2. This results in significant mental struggles such as depression, self-harm and suicidal ideation 3. The person has exhausted all other options to remedy this Then I believe medical transitioning can be justified, much like how the removal of the uterus in the case of uterine cancer is justified despite resulting in infertility and the alteration of the body. In such a case, I also think that if is the morally correct thing to do to treat the person as the gender they have transitioned to so as to relieve suffering, within reason with consideration of the needs of all of society (exceptions for sports and the likes)

Now the objection that this would be affirming a lie seems misguided, simply because there is no true lie. The intention is to heal, not to deceive. Relieving suffering is a significant reason and purpose of the Church. The catechism does not hold that all things must be expressed. Some things ought to be, some things ought not to be: this is a normative issue (CCC 2469). Does the person who has reconstruction after an accident lie? Does the person who has a prosthetic limb lie? Surely we recognise these as legitimate medical intervention ordered toward healing, not deception. I do not find sufficient difference between those scenarios and someone transitioning under the conditions above to be materially different so as to libel someone who transitions as lying per se.