I can’t imagine that the decline is related to a growing middle class and the increased rights of women, which are the typical reasons, still:
The fertility rate in Iran has been declining over the past eight years, the lowest of which was related to the past [Iranian calendar] year (March 2019-March 2020) with a birth rate of 1.2, according to the data published by the Statistics Center.
Nicholas Eberstadt, the Henry Wendt Chair in Political Economy at the American Enterprise Institute (AEI) wrote in an article in July 2020 that the fertility rate in Iran has dropped by 70 percent over the past 30 years, which has been the highest decline in human history.
https://www.tehrantimes.com/news/463759/Iran-s-population-on-upward-trend-till-2040-UN-predicts
The UN’s lowest prediction (my preference as they are very conservative) is that the population of Iran will stop growing within 20 years, and drop from 82 million to 42 million by 2100. That is 1% per year.
Iran is seemingly putting a lot of effort into reversing this, like “health insurance for infertile couples, providing services and facilities to working women, providing health and nutrition support packages to mothers and children, educational opportunities for student mothers, providing livelihood support to families, and ongoing medical services to pregnant women.” All good.
But also some policies less acceptable to the west, like reducing the age of marriage, and “employees with three to five children will be promoted”.
Net migration is slightly below zero, which of course could change, and meanwhile war can be a factor in the region. An economic reliance on fossil fuels doesn’t bode well in the long term. Basically their outcome appears to be far fewer people and a much greater reduction in income.