Interesting. I’ve never heard of that in Iran or the Soviet Union. The Arabs seem to be one up on them, cell phone divorce. No government involvement. The halala thing I don’t know, but doesn’t sound like government. Unless we consider the Imams government.
There is no separation of Imans and Government in Islam, that I can tell.
I think, in Islam, the government and the religious authorities are one, at least in theory.