Which address should change?
Distinguish the public address seen by a service from your device's local address. Changing a private IPv4 address normally does not change the public NAT address. With IPv6, several global and temporary addresses can coexist. Check IPv4 and IPv6 separately.
VPN, proxy or Tor
An internet VPN can change the exit address for traffic routed through its tunnel. A proxy affects the configured application. Tor Browser routes its web traffic through the Tor network. None of these automatically removes accounts, cookies or other identifiers; performance and application coverage differ.
Router and mobile connections
Reconnecting an internet connection may change a dynamic address, but does not guarantee it. Providers may retain addresses for long periods or use carrier-grade NAT. Switching between Wi-Fi and mobile data uses a different access network and often a different exit address. Multiple customers can still share a public IPv4 address.
Local addresses and verification
For a stable local address, a DHCP reservation is often simpler than manual configuration. Manual settings must use the correct subnet, gateway and DNS and avoid address conflicts. Compare the public IP display before and after the change using the same browser and address family. An address change alone does not prove anonymity.