No, this untrue. There is no long term harm associated with puberty blockers.
I wish the anti-trans crowd would be more honest. Just come out and say that you hate trans people, that you wish to roll-back the hard-won rights they have at the moment; that you disagree with the international scientific and medical community about best treatment; that you're happy to lie about the evidence to try to sound more reasonable and less hate-driven.
This is totally absurd. Of cause it has long therm effects whether these effects are declared as "harm" or not is subjective and whether they can be "legally" associated to puberty blockers is p much irrelevant.
It obviously has long term side effects and some are potentially unwanted and permanent.
And declaring everyone who disagrees with you as anti-trans who want to take people rights away and what not, make you the intolerant, hate-drive person you seem to see in others.