

Game works great out of the box. Just change the control layout to a community layout and you're good to go. (I picked R;N Steam controller).
Not mandatory, but adds to the experience: Get the Committee of Zero patch. It takes 0 time to install and get working. It fixes some consistency issues with the translation, translated videos and CGs, adds mouse support and auto-mode. This is the definitive ROBOTICS;NOTES experience.
Played start to finish. Visual novels like these literally feel like they were made for the Deck.
Battery time was outstanding.

d3dcompiler_47 d3dcompiler_43
Game needs d3dcompiler_47 and _43 to run with newer proton versions, using Heroic Games Launcher, umu launcher, GE-Proton 9-25 makes it work fine. Also installed the CoZ patch to enable mouse support.

Used the older Proton version 7 since that was mentioned in the CoZ documentation. Installed the CoZ patch manually (not using the "Polyversal" installer) by using the same proton instance as used by the game itself:
STEAM_COMPAT_CLIENT_INSTALL_PATH=$HOME/.steam/steam STEAM_COMPAT_DATA_PATH=$HOME/.local/share/Steam/steamapps/compatdata/1111380 $HOME/.local/share/Steam/steamapps/common/Proton\ 7.0/proton run RNEPatch-Installer.exe

Installed COZ patch. (Warning ! If you use polyversal, be sure to execute polyversal in command line and not using the explorer)
Official Controller layout doesn't work. I had to use a custom one.
Works OK except for the controls. You have to use a custom controller layout, which unfortunately means the controls shown on screen will be WASD and not controller keys. This is very unfortunate because there are QTE sections. If you're not able to quickly translate WASD controls into up/down/left/right controls, your experience will suffer from it

Use the community-submitted controller layout for Steam Controller as the official one doesn't seem to work. Install the CoZ patch (http://sonome.dareno.me/projects/rne-steam.html) using their guide (http://sonome.dareno.me/projects/coz-linux-deck.html) or by manually running the downloaded patch inside the game's wineprefix.
Does not work using Proton-GE
Installed Committee of Zero patch, had to use keyboard bindings instead of default controller mappings because they did not register.
Gameplay works perfectly, can go down to 4W TDP and 1100 GPU clocks, movies play back.
Mapped all buttons to equivalent keyboard mappings
4W, 1100 mHz
Install CoZ patch otherwise it's a worse experience than on console
I previously put a report on this last year with a slightly differant setup. Previously had to use 6.16-GE-2 GloriousEggroll with some tweaks to get it to work, but seems to just work on Proton 7.0 right out of the box, nothing more required.
No stuttering or no audio issues, just worked.
Some extra information for anyone who wants to use the CommitteeOfZero patch (https://github.com/CommitteeOfZero/rne-patch/releases) which adds mouse support and cleans up the fonts (among other things, see release notes for details) this does work on proton also. I downloaded the patch and ran (via terminal):
STEAM_COMPAT_CLIENT_INSTALL_PATH= STEAM_COMPAT_DATA_PATH= run RNEPatch-Installer.exe
For Example: STEAM_COMPAT_CLIENT_INSTALL_PATH=/home/username/.steam/steam STEAM_COMPAT_DATA_PATH=/Games/Steam/steamapps/compatdata/1111380 /Games/Steam/steamapps/common/Proton\ 7.0/proton run RNEPatch-Installer.exe
With this I was able to install the patch, I'm still a bit of a Linux noob and this took me bit of time to figure out so hope this helps someone out who was in the same situation as me! :)
Its a good game and works fine most of the time.
Crashes sometimes, but can get past them by reloading from prev saves. Save often. Always crashed for me in the movie library and CG library. Seemed like it crashes less in windowed mode tho.
After completion of some phases, when game loads main menu, the screen text and some assets are missing. Works fine after restarting the game. (At this point I had installed the zero patch so it could be the reason)
Install committee of zero patch. It improves the game significantly. Use proton 6.3-6 (that's what worked for me), install vcrun2017 (using winetricks) and the patch. (In the patch setup, I also had to manually choose the game directory.)

6.16-GE-2 GloriousEggroll
Installed the game no problem but it wouldn't start. Forced comparability mode to "Proton-6.14-GE-2" which got me further but would black screen and close right after the production logos. I added
PROTON_USE_WINED3D=1 %command%
to the "Launch Options" and boom! Was able to get into the game and load a save. Audio and visuals looked fine from the 15 or so mins I tried it out. Will play for much longer later and report back and issues faced.
Works quite well overall out of the box
At one specific point in the game, the game crashed repeatedly. However, the crashes weren't entirely consistent - meaning if I crashed, I could reboot the game, and the game would actually crash further than the first time, so by spamming saves and loading after crashes I got passed this difficult moment. Only happened in one specific section of the game, not all the time
Didn't finish the game because of plot issues (playing Chaos;Head first is apparently recommended), but no big issues outside of the crashes for the time I played
in order to run this game without crashes you need to install the latest vcrun on your Proton environment. For instance i used protontricks for this (ex: protontricks 1111380 --force vcrun2019).
also, you can apply the Committee of Zero's patch by running this command:
cd <<path of .exe>>; STEAM_COMPAT_DATA_PATH=~/.steam/steam/steamapps/compatdata/XXX/pfx ~/.local/share/Steam/steamapps/common/Proton\ XXX/proton run RNEPatch-Installer.exe
On Steam in the game properties, set:
=== General Tab ===
[ Disabled ] Enable the Steam overlay while in-game
[ Disabled ] Use Desktop Game Theatre while SteamVR is active
=== Compatibility Tab ===
[ Enabled ] Force the use of a specific Steam Play compatibility tool
"Proton 5.0-10"
Open a terminal and run the following commands either one-by-one or by copy & paste.
https://gist.github.com/Zi-SH/a40f2f13d93fe37e7919d3d02d407782
Fully completable with default proton, though an extra flag is advised to prevent crashes
There are multiple moments in the game where it consistently. On average, there is about 1 such moment in each chapter. There is nothing specific about them, they are not linked to any specific game event or resource; but it is deterministic and 100% reproducible, so it won't progress after restarting.
A workaround that works for me is disabling DXVK with PROTON_USE_WINED3D=1
. However, graphics are degraded in this mode (severe aliasing on character models, config menu not rendering); so I recommend to play with default settings, save frequently and only restart the game with this WINED3D enabled to get through these crash-prone areas, and fall back to default settings soon afterwards.
The game has a fast-forward feature so that catching up to the crash point is very quick even if you don't save too often.
The "Committee of Zero" fan patch can be installed by running a custom executable with game's wine prefix, and it works very well.
Can't progress further than Chapter 1.
Consistently crashes around the end of Chapter 1.
I switched to Windows afterwards.

crashes instantly
Launcher works, but when starting the game a black window appears for a fraction of a second, then closes

Game opens and runs, crashes within 1-3 minutes
Sometimes will get to actual gameplay, but it never makes it longer than 3 or 4 minutes.
Game runs fine out of the box.
Note that the game itself does not support mouse input and does not appear to recognize Steam Gamepads correctly on Linux.
Started the game up and played around with settings + started a new game with absolutely no problem at all.

Game starts, but does not get to main menu.
The game does indeed start, but after going through all the logos it just crashes.