Big-ticket items like PS5s and laptops have serial number barcodes on the outside of the box for that reason.

If you really don't want it tracked for some reason, buy from a third party seller who, while they might record that info, isn't going to share it with anyone and will probably lose the sticky note it was written on in a few weeks. Or go to a pawn shop and buy one in cash.

But if you're going to use a PS5, aren't you going to have to link a payment method for stuff like online services anyway?

I'd be surprised but perhaps my information is just out of date. They do need to make sure you return the correct model but typically that's done by visually verifying what you return matches what was sold. This can be problematic which is why you sometimes here about people having returned bricks instead of the proper item at Walmart.

Though, a PS5 may have been a bad example because you do tend to reach certain price points were things differ. Like CPUs typically are kept track of individually, though GPUs often aren't.

I used to work for one of the big game retailers in the UK, and we didn't do that, we would just scan the generic barcode. That was about 15 years ago though, so things may be different now.