In settings under steam play there's an option to enable games that aren't whitelisted, perhaps it somehow got unchecked?
Hello @swhilsmier, this reads like #6501. What version of Proton is the game configured to use? In Steam's library view, please select the game, then the ⓘ button on the right side. There should be a line in the additional details with something like "Runs on this computer via Steam Play. Proton # selected by you for this title". Enabling Proton can be controlled either in the global settings or in the per-game properties.
This is what my settings were:

I made some changes to see if it was the global settings:
The issue seems to be with Proton Experimental. Let me know if there is any other testing you want me to do or a log file to pull.
I think this same issue is happening to me. I'm not sure if it's a Proton-GE issue or Steam. It just started for me. I haven't run updates since the last time I played, though. I ran updates as a troubleshooting step. I can't launch FO4 with Proton-6.18-GE-2 anymore even though it was working last week. Proton-6.20-GE-1 also doesn't work. Proton 6.3-7 works fine, but I don't get a lot of audio in the game, which is a different issue.
I used Timeshift to restore my system to a time before the last time I played, but the issue still remains.
I started Steam through the terminal, and I'm seeing this whenever I try to open Fallout 4:
Application could not be started, or no application associated with the specified file.
ShellExecuteEx failed: File not found.Application could not be started, or no application associated with the specified file.
ShellExecuteEx failed: File not found.

Operating System: Linux Mint 20.2
KDE Plasma Version: 5.18.5
KDE Frameworks Version: 5.68.0
Qt Version: 5.12.8
Kernel Version: 5.11.0-38-generic
OS Type: 64-bit
Processors: 24 × AMD Ryzen 9 3900X 12-Core Processor
Memory: 15.6 GiB of RAM
Steam client version (build number or date): Oct 13 2021
Distribution (e.g. Ubuntu): Linux Mint
Opted into Steam client beta?: Yes and no
Have you checked for system updates?: Yes
Hello @TromboneSteve, this issue report is focusing on the Steam client's play / install button behavior. Any quirk behavior with a third party Proton build should be pondered by the maintainer of the that third party Proton version, or if you can reproduce the same behavior with a mainline Proton version, then on the game's compatibility report in the Proton issue tracker.
proton 6.3-7x2 2021-11proton 6.18-ge-2x1 2021-11proton 6.20-ge-1x1 2021-11proton 6.19-ge-2x1 2021-10proton experimentalx1 2021-10
I am no longer able to launch FO4. Just a week or so ago, I was able to play it without any issues using Steam Play, but now the "Play" button turned into a gray "Install" button that says "Available for [Windows]" next to it. All of my other games in my library appear to be downloadable/installable on my Linux computer or are still playable.
I disabled Steam beta to see if that would change anything, but there was no effect. I submitted a ticket with Steam Support, but they said to post the issue here. It seems like a Steam client issue rather than a Proton issue though.
Operating System: Manjaro Linux
KDE Plasma Version: 5.22.5
KDE Frameworks Version: 5.87.0
Qt Version: 5.15.2
Kernel Version: 5.14.10-1-MANJARO (64-bit)
Graphics Platform: X11
Processors: 12 × AMD Ryzen 5 3600 6-Core Processor
Memory: 15.6 GiB of RAM
Graphics Processor: Radeon RX 580 Series