Are you confusing “ports” with “interfaces”? I can see that happening since we do colloquially refer to both as ports depending on context.

Each service will bind to it’s own “port” which is tied up by that service. However each interface (the external physical connection) supports like 65,000 software ports.

So in practice, no, you don’t usually need more than one physical network connection to run multiple services.

I don’t remember Valheim specifically, but most standalone servers don’t require you to own the game in the account you use to host it

I’m sure it’s also doable via your own vps, but I think most people are talking about managed systems like cloudflare tunnels https://www.makeuseof.com/use-cloudflare-tunnel-expose-local-servers-internet/