The system starts, I can login as root, no errors found, but :8123 is not reachable.
The varnish vm is running, and the message “Home Assistant started” is shown before OS login. But I don’t know if something else should be started, or if occured any error I am not seeing.
I’m most definitely not a networking expert, but it doesn’t seem like you are specifying a bridge (or any other network configuration) in your virt-install command. I think you need to specify at least something. See e.g. the manual.
How you would set that up on Gentoo, I don’t know, but maybe the gentoo wiki networking page would be a good place to start?