If your Calibre server goes to sleep. Zzzz to access.
If your
wired Laptop can be made to support WOL (wake on LAN) and you can send
it the 'Magic packet' from your readers, you should be good after a short pause for the
server to come awake fully. (No don't ask me how to do this

)
Your phone is NOT WiFi on your LAN, so that IP will not work.
You would need to find your WAN IP (it is dynamic. It changes ) of your router and also set Port forwarding to the Server IP.