A Working Local Proxy Can Keep the Same Public IP
Explain why a loopback proxy using the same machine and network path does not automatically provide a new outward identity.
A proxy can work correctly while a website still sees the same public IP. Running the proxy on the same computer, using the same network route, gives it no automatic reason to leave through another address.
The loopback endpoint is where the application reaches the proxy. It is not a public exit address. The proxy then opens a destination connection under its own host's networking policy.
An SSH dynamic forward to the same machine illustrates the distinction: it supplies a SOCKS interface, but the destination connection still originates from that machine. Its router or provider can translate the source exactly as for a direct request.
To obtain a different exit, the setup needs a different outward path or an explicitly selected usable source address. An extra local port alone does not supply one. For public requests allowed through a public intermediary, the free proxy list offers remote candidates; verify their actual exit rather than assuming it from the listening address.
Decide whether you need a proxy interface, filtering, or a changed public identity. Those are different outcomes; only the last requires the final outward address to differ.