As a Podman user, I expect documentation accurately reflects the current state of the software, so I am aware of its limitations.

Briefly: Podman added support for network aliases in v2.2.0 (and up). However, this support has significant limitations at present, documented in https://bugzilla.redhat.com/show_bug.cgi?id=1896487 (particularly in the last few comments) - specifically we do not allow Podman to use network aliases for more than one network at a time (the first network the container is connected to is the only one where aliases work). We are working to resolve this for a Podman release that should come alongside 8.5.0 or 8.4.1, but versions of Podman in 8.3.1 and 8.4.0 will ship with this limitation and should have it documented.