The new law that bans gender-affirming care for minors also mandates that adult patients seeking trans health care sign an informed consent form. It also requires a physician to oversee any health care related to transitioning, and for people to see that doctor in person. Those rules have proven particularly onerous because many people received care from nurse practitioners and used telehealth. The law also made it a crime to violate the new requirements.
Another new law that allows doctors and pharmacists to refuse to treat transgender people further limits their options.
Calling the Nazis far right is ignoring that their politics were more complicated than a simple 2D spectrum. They adopted ideas from both left and right.
They certainly adopt rhetoric from the left which helps them get elected, then enact exclusively right-wing policies when they actually have power, sure. Fascists usually use populist rhetoric to get into power but then they never do anything to actually reduce inequality (because that would be the opposite of fascism).