

How much experience do you have with networking, exactly?
The DNS record points to a private IPv4 address (10.0.0.41), which cannot be accessed from the internet for multiple reasons; first of which is that it’s almost certainly behind a NAT gateway.
Your internet provider has given you a single publicly routable IPv4 address and assigned it to the WAN interface on your modem or router. If you want to access a host on the LAN, you’ll first have to configure port mapping or port forwarding on the router. Then you’ll have to open holes in your firewall and accept the fact that every bad actor will try to break into that host unless you know how to set up network security.
The most straight-forward method would be to buy a standalone switch. I have a TP-LINK TL-SG108 8-port gigabit switch and it seems to retain the ARP table indefinitely.
My previous solution was an ESP32 board with an SSH server and a relay, wired parallel with the power switch, that would be closed by an output pin on command.