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:
# Save the umask and set strong permissions
echo $"Setting up Steam content in $STEAMDIR"
Towards the end of the script there is the function check