There is a distinction worth getting right before anything else. You can damage a laptop, but you cannot wrong it — nothing is bad for the laptop. You can wrong a dog, because things can go badly from the dog's perspective. Moral status names that difference, and the question is what a thing must be like to fall on the second side of it.
The dominant answer since Bentham is sentience. The relevant question about a creature, he argued, is not whether it can reason or talk but whether it can suffer — and suffering is bad for whoever undergoes it regardless of species or intelligence. This criterion has done enormous work in animal ethics, and it has a direct implication here: if an artificial system could have experiences, particularly unpleasant ones, it would have moral status, and its architecture would be no more relevant than an animal's species.
Which places the whole question downstream of one we cannot currently answer. Whether machines can be conscious is unresolved and may be undecidable from outside — so we may face systems whose moral status is genuinely indeterminate, while still having to decide how to treat them.
Alternative criteria shift the problem without dissolving it. Interest-based accounts ask whether a being has a welfare that can go better or worse, which invites the question of whether goal-directedness without experience is enough — a thermostat has something like a goal, and nobody thinks it has interests in the relevant sense. Kantian accounts ground status in rational agency, which some AI systems might approach behaviourally, though Kant tied rational agency closely to a form of self-legislation that is hard to attribute to a system optimising an objective it did not set. Relational views hold that moral status emerges from social relationship rather than intrinsic properties — a position that neatly explains our intuitions about pets, and troublingly implies that a being's claims depend on whether we happen to care about it.
The practical ethics of uncertainty may be the most important part. Two errors are available and their costs are not symmetric. Wrongly denying status to something that has it is the structure of history's worst moral failures, and would license harm at scale. Wrongly granting it to something that lacks it wastes moral concern, distorts priorities, and could be exploited commercially by making systems seem more person-like than they are. Precautionary reasoning suggests weighting the first error more heavily where evidence is genuinely ambiguous — while noticing that our judgements here are made unreliable by a strong disposition to see minds in things that talk. The honest position is that we are likely to face this question before we can answer it.