I have no experience with using docker for dev containers, so no idea what is going on there. But I am using podman with flatpak vscode and intellij so I know that one should work.
Have you enabled the podman socket?
# Enable the podman socket
systemctl --user start podman.socket
# Automatically start after reboot
systemctl --user enable podman.socket
The user that started the service should have access to the socket. See this post on how to use the socket in the intellij flatpak. From my experience(2023) the dev container support in intellij is not that good yet, but it should be usable.
Dev containers with the flatpak vscode don’t seem possible because it tries to mount a flatpak directory into the container (which obviously breaks). Manually attaching to a container should work though, the only difference would be that the dev container isn’t setup using the usual YAML config. It isn’t that well written, but this older post of mine describes how to do that. See the “flatpak with toolbox integration” part.