In general, the packaging does not have to be kept. But if you have small items like watches or CPUs etc. it makes sense because you might want to sell them again and the original packaging would be helpful. But it is not necessary for the warranty alone. However, it should be well packed for the return shipment. Otherwise it might not be accepted.

It would be better to still have the packaging. But with warranty, I don't think you'll need it unattended. If you return the item without packaging or damaged, you will not be refunded the full price.

I had a warranty claim with a toner cartridge, I was able to dispose of the defective one straight away and the manufacturer sent me a new one.