Yeah, I don't think the strike on Iran shed as much light on this question as I'd originally thought it might, but it still seems clearly to be the case that air defense is not a big part of the Axis of Resistance strategy. Ansar Allah fought an open war against Saudi Arabia in the mid-late 2010s, during which the Royal Saudi Air Force routinely flew over Houthi-held territory, and so far as I know they've never verifiably shot a flight down.
Again, I think the most useful model here is Lebanon. Hezbollah has a desultory complement of SAM launchers, but no meaningful control over its airspace.
Oh yes that's just absolutely fanciful boasting by the Houthis.
The Houthis were probably not far off from claiming to have shot down the Ingenuity chopper which NASA lost on Mars . In reality they can't shoot down a Cessna 172.
Again, I think the most useful model here is Lebanon. Hezbollah has a desultory complement of SAM launchers, but no meaningful control over its airspace.