I think you have at least two alternatives
Alternative 1: Connecting via Unix domain socket
If you could have Postgres listen on a Unix domain socket, you could then pass in that socket to the container with a bind-mount. Use podman run with one of the command-line arguments --volume or --mount.
Maybe something like:
--mount type=bind,src=/path/to/socket/on/host,target=/path/to/socket/in/container
If your system has SELINUX enabled, you would need to add the option Z
--volume /path/to/socket/on/host:/path/to/socket/in/container:Z
Alternative 2: Connecting via TCP socket
I think you could add the option
--network slirp4netns:allow_host_loopback=true
to the podman run command and connect to the IP address 10.0.2.2.
Quote "Allow the slirp4netns to reach the host loopback IP (10.0.2.2, which is added to /etc/hosts as host.containers.internal for your convenience)" from the podman run man page.
See also slirp4netns.1.md.
(The IP address 10.0.2.2 is a default value hard coded in the source code of slirp4netns).
Here is an example of a container that connects to a web server running on localhost:
esjolund@laptop:~$ curl -sS http://localhost:8000/file.txt
hello
esjolund@laptop:~$ cat /etc/issue
Ubuntu 20.04.2 LTS \n \l
esjolund@laptop:~$ podman --version
podman version 3.0.1
esjolund@laptop:~$ podman run --rm docker.io/library/fedora cur-l -sS http://10.0.2.2:8000/file.txt
curl: (7) Failed to connect to 10.0.2.2 port 8000: Network is unreachable
esjolund@laptop:~$ podman run --rm --network slirp4netns:allow_host_loopback=true docker.io/library/fedora curl -sS http://10.0.2.2:8000/file.txt
hello
esjolund@laptop:~$
