https://github.com/Percivalll/Copy-Fail-CVE-2026-31431-Kuber... - This PoC has a good example of how Copy Fail might have an impact in a container based environment, it's exploiting the shared layers in a pair of container images, to overwrite a file in one image based on the running of an exploit in another.
Whilst I've not directly tested podman for that kind of attack, I'd be a bit surprised if it stopped it, given how this vuln works.