Might just be me, but the above seems to be a serious mis-reading of the situation as well as the very real potential issues that a RAN
ANZAC-class frigate could run into if deployed in/around the Strait of Hormuz, the Persian Gulf and/or Gulf of Oman.
The upgraded radar system should be quite good at detecting aerial threats at elevation, but will likely still encounter problems detecting small, low-flying aerial threats, with some of the smaller drones being potential examples. AFAIK the RAN frigates do not have the ability to participate in CEC targeting, so the ability to get advanced warning from other offboard assets would be more limited than might be possible aboard the RAN DDG's.
This could become a significant problem given the volume of strikes Iran has been launching, though as time marches on, Iran's ability to have such a volume of missile and/or drone attacks will likely decline. From news articles dated 2 March, there was reporting that over 1,000 drones had been launched by Iran at targets around the Gulf. From
this story in the Guardian, the UAE had been targeted by 689 such drones, and downing approximately 94% of them, with 44 getting through. However, that is sort of the issue. The RAN frigates only can carry and launch up to 32 ESSM before the VLS is empty. Now it would be unlikely that Iran would target a RAN frigate with such a large volume of drones, but even the leakers through UAE air defences would be sufficient to completely exhaust the VLS and still have leakers. If such a frigate was deployed to escort shipping like tankers, the RAN might find itself needing to make daily (or even several times per day) port calls just to reload the VLS.
There is also the reality that all Iran would need to do to overwhelm any air defence umbrella that an
ANZAC-class frigate might provide for itself as well as nearby shipping would be to simply launch 33+ drones, something which IMO Iran has certainly demonstrated an ability to do.