It's deterministic. They throw in a random seed with online services like chatgpt.
If it wasn't deterministic for some reason thar wouldn't be because it's magic, it would be because of hardware timing issues sneaking in (same reason why source code compiles can be non-reproducible), and could be solved by ordering the results of parallel computation that doesn't have a guaranteed order.
To the best of my knowledge it's not a problem though.
Are humans deterministic? Hell, I wish my plain old normal digital computer was 100% deterministic, but it ain't due to any number of factors from bugs and state logic errors all the way to issues occurring near the quantum level.
You're setting the goal so high it is not reachable by anything.