This proposed law goes even further than what you've described. Besides criminalizing gender-affirming care in Florida and making parents in Florida subject to criminal penalty if they allow their transgender children to receive gender-affirming care, the law authorizes Florida judges to overturn child-custody decisions made by judges in other states if the child is receiving gender-affirming care in the other state.

The bill literally incentivizes non-custodial parents in Florida to kidnap their children in other states, to bring them back to Florida to have the custody order vacated on the grounds of the child receiving puberty blockers or hormone therapy. (The bill also mentions surgery, but that's a classic red herring.)