WAN side IP Not updating upon Ethernet plug is unplugged and plug from another provider

I can assume none of your devices use DSA - if you have the Switch page in the Network menu then it doesn't.

When that is the case, wan is not connected directly to the physical port, instead, it is connected to a switch.

When WAN port goes through a switch, the actual network interface doesn't see that it is connected or disconnected, and while it has a valid DHCP lease it won't request a new one. This topic and parsing /etc/board.json can possibly help you, but some coding is needed for sure.