Ansar Allah is an operational arm of the IRGC, with devolved autonomy over local matters --- approximately the same relationship an American state has with the federal government. What's your issue with "Iran-backed"? They're explicitly Khomeinist and most definitely are backed by Iran.

I think people read things like "Iran-backed" and immediately frame it in terms of US/Iran conflicts, but GCC/Iran conflicts are the more salient geopolitical frame, at least until like last year.