

MAC address is in the data link layer of the networking stack, and would only be seen by other devices on the same network as you. This isn’t visible to websites you visit (unless you’re on the same subnet), and as TCP packets go through network hops, the MAC address is replaced with with the routers MAC address for each hop.
The reason for MAC address randomization (standard on iPhone and Android) is not for anonymity to the websites you visit, but is there to anonymize the wifi broadcasts in your general vicinity, like a 30 meter radius. The MAC address is randomized so that broadcasts to check wifi networks while you’re out and about can’t be used to track your physical location.
See also: why you don’t wear a condom someone else came in