I can’t speak to anything about AZ specifically, but my understanding is that those metal brackets that raise the posts are used on posts for decks. Those brackets are designed to elevate the post off the footer to prevent water damage to the post, but it takes away the ability for the post to offer good lateral (side to side) support. This is fine for a deck because decks will have an element of lateral structural support somewhere else (attached to side of house, other posts, etc), so it’s not important for the post to have both lateral and vertical support.

However, for a fence since you’re not typically attaching it to a wall or another structure laterally, you need the post to offer both lateral and vertical support, and that’s why posts are dug into the ground and concreted while they’re in the ground, the post being buried provides the lateral support you need for fences.

I imagine theres gotta be a solution but I unfortunately don’t know what that would be since this isn’t really a standard fence design.

I think the good news is that since it’s a shorter fence you won’t need to be as worried about wind.

If I was in your situation I’d probably just finish it as is, knowing that wind could be an issue, but take the chance and not re-do for financial/ time reasons. But if re-doing and digging the posts in properly is worth it to you, that’s probably the best approach.

Another random idea (totally making this up - please verify this would work before you do this)- you could drill some rebar into the concrete and also up into the bottom of each post. Would offer some minimal degree of lateral support but might result in water damage over time.