Hello @xor-bits, this was pointed out at https://github.com/ValveSoftware/steam-for-linux/issues/9447#issuecomment-1592231506. The key detail being that these xdg-desktop-portal backends do not implement a file chooser interface. Report this missing functionality to the individual backends.
From the Steam client side, #9584 covers what Steam should be doing in this scenario.
Closing as not a Steam client bug.
Your system information
Please describe your issue in as much detail as possible:
The native file picker doesn't work on Hyprland and possibly other xdg-desktop-portal tasks won't work either. This seems to be because steam supports only xdg-desktop-portal-gtk and xdg-desktop-portal-kde portals but not xdg-desktop-portal-wlr or xdg-desktop-portal-hyprland which Hyprland uses.
Steps for reproducing this issue:
Add a Game>Add a Non-Steam game...>Browseor
Steam>Settings>Storage>+