That's not typically how this works. A specific item, e.g. a specific PS5, is rarely ever tied to a new purchase. There's no reason for it. They don't care that a specific PS5 was sold to someone. Just that a PS5 was sold.
However, there are exceptions. Pawn shops for sure. They keep track of those IDs because they have to make sure things that are pawned aren't stolen. So they check databases when acquiring goods to make sure. When you purchase a PS5 the receipt is for a specific PS5, for similar reasons. If something gets reported as stolen they can track it down.
Broadly speaking, if you're worried about a company knowing exactly which PS5, or whatever you bought, I wouldn't. Amazon and Ebay certainly have no clue. Amazon would have no way of knowing what item you purchased cause they don't know which one in the warehouse will be packed. There's no reason for them to keep track of things like that.
Of course, a wide variety of things can be purchased on these sites so there may be exceptions to this, such as vehicles. Don't know if that's still around on ebay but those would almost certainly be for specific VINs.