oberon

Your steam installation in Flatpak should have a bin_steam.sh in /../com.valvesoftware.Steam/current/active/files/lib/steam. Also a bootstrap.....tar.xz file.
The script unpacks the bootstrap file in a .local/share/Steam directory. The bin_steam.sh script tells you where it installs around line 95:
function install_bootstrap()
{
        STEAMDIR="$1"
        # Save the umask and set strong permissions
        omask="$(umask)"
        umask 0077
        echo $"Setting up Steam content in $STEAMDIR"
 
Towards the end of the script there is the function check_bootstrap(), which checks that the bootstrap was unpacked successfully. Basically you can manually unpack the bootstrap file in the right place:
tar -xf bootstrap.tar.xz and remove the checks in the script and it should execute and run.
 
Make sure that the partition that has the bootstrap etc ($STEAMDIR) is mounted with the exec permission in /etc/fstab !
That's it - voila, it should run now....