Flatpak gives warnings not present on normal distribution

Arch (`ruffle-nightly-bin` AUR package):

Flatpak:

Errors exclusive to the Flatpak:

> 2026-02-09T15:29:23.049653Z WARN ruffle_desktop::app: Gamepad support could not be initialized: No such file or directory (os error 2)
> 2026-02-09T15:29:23.117918Z WARN egui_winit::clipboard: Failed to initialize arboard clipboard: Unknown error while interacting with the clipboard: X11 server connection timed out because it was unreachable

First error goes away when granting `device=input` to the Flatpak. The second I don't know how to fix.

Start by comparing the attached Arch and Flatpak logs, then inspect the Flatpak sandbox permissions related to device input and X11 clipboard access. The payload names no files or tests; done means identifying a fix for the clipboard warning and confirming the reported Flatpak warnings no longer appear.

Written by the indexing model from the issue text.