It won't work, flatpak is sandboxed. You have to use the distro package to access hardware.
Hello @hikagura99, are you still experiencing this issue on an up to date system? It looks like you're responsible for providing the steam-devices udev rule set if you're not using a Steam system package that would provide it. (From https://github.com/flathub/com.valvesoftware.Steam/wiki#my-controller-isnt-being-detected)
Closing pending feedback.
Nothing extracted yet.
Your system information
Please describe your issue in as much detail as possible:
I changed from official repos to flatpak version of steam since i had some problems with proton, which have been solved, but the client doesn't recognize my DS4 anymore, both if plugged via cable or via bluetooth.
Steps for reproducing this issue: