“There is not a native app on Steam deck today,” said Andrew Fear, GFN boss, back in January. “Use a Chromium browser to make it work. I would say that both Nvidia and Valve, I think we’re both interested in making [GeForce Now on Steam Deck] better. But we don’t have any announcements on a native app coming to Steam.”
The weird Chromebook situation is clearly a result of them shutting down Stadia when other teams were still intending to integrate with it.
Perhaps the Chromebook executables can be made to work on Linux?