Permission denied within mounted volume inside Docker/Podman container
Thanks to the people here, the solution is quite simple (but not obvious):

My GNU/Linux container host has SELinux activated, and that's why I was having permissions problems. The solution is to simply append a :z to the podman run volume argument so that this:

podman run -it -v /host/foobar:/src_dir /bin/bash

becomes this:

podman run -it -v /host/foobar:/src_dir:z /bin/bash

That's it.