Your source is a decade old. The situation has deteriorated in practice after the 2022 protests, with the regime seeing trans people as connecting with the broader Western lgbtq+ movement and so "importing harmful ideas". Source from last year: https://uprdoc.ohchr.org/uprweb/downloadfile.aspx?filename=13540&file=EnglishTranslation
In general, it's not that Iran recognizes "trans people". There is no (officially allowed) trans identity. Medical and surgical transition is allowed as a way to "smooth a flaw" and assimilate into cishet-normative society. It is often applied as a way of state-sponsored conversion therapy: https://www.nytimes.com/2025/10/10/world/middleeast/iran-transgender-surgery.html