The user namespaces restriction does affect gnome-control-center too.
This is what I get when I try to set a local picture for the user account.
20:19:40.0120 GLib: DEBUG: posix_spawn avoided (fd close requested) (child_setup specified) 20:19:40.0124 GnomeDesktop: DEBUG: Failed to launch script: bwrap: No permissions to creating new namespace, likely because the kernel does not allow non-privileged user namespaces. On e.g. debian this can be enabled with 'sysctl kernel.unprivileged_userns_clone=1'.