Steam Flatpak attempts to install games to `/usr` directory on Arch Linux

Hi,

I am using the Flatpak version of Steam on Arch Linux. When I try to download/install a game, Steam attempts to set or use the `/usr` directory as the installation path, which leads to permission errors.

What I have already tried:
1. Deleted the `libraryfolders.vdf` file to reset library configurations.
2. Navigated to Steam Storage Settings and manually selected the default download location.

Despite these steps, the issue persists and Steam still tries to use the `/usr` path.

System Info:
- OS: Arch Linux
- App: Steam Flatpak (`com.valvesoftware.Steam`)

Start by reproducing the installation attempt in the Steam Flatpak app com.valvesoftware.Steam on Arch Linux, then inspect the library configuration represented by libraryfolders.vdf and the Steam Storage Settings location. Done means determining why /usr is selected and establishing a writable game installation path instead.

Written by the indexing model from the issue text.