Yes, of course ping can traverse the internet. But you are pinging a public IP address.
You can ping your own public IP address, of course. And you can ping your own local devices on your LAN when you are connected to that network.
However, you cannot ping your LAN devices from the internet because they do not have a publicly routable IP address. It seems as if you are trying to find a method to be able to ping your individual LAN hosts from the internet... this is not possible (but if you need to be able to do this, you can setup a VPN or similar to allow you to tunnel into your local network0.