This is one thing I really like about Flatpak, never having to worry about missing or broken dependencies. Totally worth the bigger install size imo.
One thing to note if you go this route OP: If you use Steam Input, you’ll also need to install the steam-devices package (game-devices-udev on Arch), or setup udev rules manually. Flatpak still doesn’t let apps do this automatically as far as I’m aware, but it’s smooth sailing aside from that.