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How agents handle out of stock products
An agent that is told a product is available and then cannot buy it does not try a different variant, it moves to another store. That makes accuracy in the negative more valuable than accuracy in the positive, and it is the case almost nobody tests, because the person checking is looking at a product that happens to be in stock.
An agent that is told a product is available and then cannot buy it does not try a different size or look for an alternative in your catalogue. It leaves. That single behaviour is why accuracy in the negative matters more than accuracy in the positive.
The test nobody runs
Availability data is usually correct in exactly the case where it is easiest to check: a product that is in stock, verified by someone who can see it is in stock.
An availability field populated from a truthy check is correct precisely while the answer is yes, and wrong the moment it matters. Test with a product that is out of stock. See how to expose stock availability to agents.
Variant level, not product level
A shopper asks for a specific size. "The jacket is available" answers a question nobody asked, and the agent either proceeds and fails at the variant picker or treats your data as unreliable.
Availability belongs on the variant, alongside its own price and identifier. See no variant data.
The states that are not in stock
Backorder, preorder, discontinued and available to order are all different from in stock, and collapsing them converts an honest answer into a failed purchase. An agent that knows an item ships in four weeks can make a decision; one that discovers it at checkout has spent the attempt.
Why the cost compounds
A single wrong availability costs an order. A pattern of them costs more than that, because it makes your published data less useful generally, and the value of your feed rests entirely on it being reliable.
Questions
Should I hide out of stock products?
Better to state the status accurately. A product marked unavailable is a clean answer that costs you nothing. A product marked available that cannot be bought costs you the attempt and the shopper.
What about backorder and preorder?
State them as themselves rather than collapsing them into in stock. An agent buying for somebody who needs an item this week treats a four week backorder as a failure, and finding out at checkout wastes the attempt.
Does an out of stock product hurt my store overall?
An accurately marked one, no. A pattern of availability that turns out to be wrong is more damaging, because it makes your data less useful to rely on generally.