When you are outside your home WiFi network, are you connecting to the external address of your router or are you trying to use the internal address of your calibre server? If you type "whats my ip" into a Google search, it will return your external address.
Most often your home computer will have a private IP address, for example, 192.168.58.12 while the router will have a public address, for example, 102.45.68.107. See RFC 1918 for more information or simply search "private IP address".
On my wireless router, I enabled port forwarding from the router's external IP address to my calibre server's internal address for port 8080. Setting this up varies with the router manufacturer and between devices from the same manufacturer.
I use a dynamic DNS service to generate a human readable address from my dynamic IP address (the ISP changes it at random intervals). Currently, I think I'm using
Duck DNS (
*). However, using the external IP address should work for testing.
* The reason I'm not certain about DuckDNS is that I've been switching between several providers since the last site I used went out of business with no notice.