There's two supported ways to run Home Assistant:
- Home Assistant OS
- Docker container
In both cases, it's running on its own IP address, so nothing else will be using port 80.
With Docker, you'd normally either use its standard NAT network, or bridge it to your LAN using a macvlan or ipvlan network. Bridging is usually better because some devices rely on broadcasts.
You used to be able to run Home Assistant directly on an existing Linux system, but that's been deprecated for over a year and unsupported since December last year.