Know that doing this is not advised and your computer will now be directly accessible to the Internet. As long as you're fine with the potential for vulnerabilities and that risk or just don't care:

You need to setup port forwarding on the local router for the computer you want to connect to and check the docs for origin_web_ui to include "wan" (Internet). Docs also describe encryption configurations. https://docs.lizardbyte.dev/projects/sunshine/latest/md_docs_2configuration.html#port

Know that your network router (like 192.168.1.1) keeps everything on your network from receiving any connections that weren't already requested by a computer or phone on your network. Port forwarding opens a hole into your network and that computer now has to protect itself so keep it updated, especially sunshine, and I'd recommend not turning off ufw but just adding some rules to allow the sunshine traffic.

I may be assuming here, but I did not see it mentioned.

With the setup you have it will not work. Just having a public IP does not tell your router what internal device and port to send the traffic to and your router is not going to allow this. You would need to forward that port internally into your network.

However, DO NOT DO THIS! You do not want to allow traffic from the public internet into your computer. You are asking for trouble.

I am going to solution this without ever having done it, so cut me some slack.

You should look at something like tailscale. Tailscale allows you to create a custom wire guard vpn that allows you to connect to a device running tailscale from the public internet. I think you can have 3 account for free. Once connected to tailscale, you will see devices on the tailscale network and their relative IPs to the tailscale network. Connect to that IP and port and that should allow you to connect.

Use a VPN like zerotier or tailscale to connect to your game host server.

This will punch through your firewall and it won't expose your server to the raw internet