Arduino Ethernet Shield 2: How can I automatically determine the MAC Address?
No, the W5500 chip does not have a mac address. You can give it any mac address that you want. The router might not like some mac addresses though.

There are online mac address generators.

The sticker with the mac address is an extra service. It is unique number. But it is just a number on a sticker, it is not related to that specific shield.

Often the mac address DEADBEEFFEED was used. But when two different Arduino boards use the same mac address, the router thinks it is the same device. When there are two devices with the same mac address at the same time connected, that is for sure a way to mess up the router.