Oh damn, you're using the snap version of Steam, this is unfortunately outside of my area of experience :(
Some key error messages I see are:
/home/pokko/snap/steam/common/.local/share/Steam/ubuntu12_64/steamwebhelper.sh: line 53: /proc/sys/kernel/unprivileged_userns_clone: Permission denied
/home/pokko/snap/steam/common/.local/share/Steam/ubuntu12_64/steamwebhelper.sh: line 60: /proc/sys/user/max_user_namespaces: Permission denied
and
flock /usr/share/fonts/truetype/liberation/LiberationSans-Regular.ttf LOCK_SH failed. errno = 13vkEnumeratePhysicalDevices failed, unable to init and enumerate GPUs with Vulkan.
BInit-Unable to initialize Vulkan!
You've got permission errors and a GPU driver issue somewhere, likely related to the permission errors. The flock errors stand out to me also, as they are fonts. Maybe required fonts for the game to run?
I don't have any idea about your hardware issues. They're likely unrelated if the game has already been played without issue.
For the steam diagnosing, start with running steam from your terminal, by running steam. You may get lucky and the error is clearly identified in the console.
If that fails, backup $HOME/.local/share/Steam/steamapps/compatdata/221100 - the 221100 is the app ID of of DayZ on the steam store. After backing it up, delete the original 221100 directory and re-launch the game. This doesn't delete the game, but rather deletes the Proton prefix for the game.
If the game launches, copy any save files (if any) you may have in the backed-up 221100 directory over to the new one.
The above worked for me when I had similar issues when playing Batman: Arkham Asylum.
To be thorough, have you tried any other games to rule out your hardware being an issue?
Thankfully someone stepped in about snap... I don't like it and would have gone on a rant without circling back to the issue on hand lmao
As recommended somewhere up the chain, try a different version of Proton. Support for your hardware may have been deprecated.
From here, I'm out of my element. Best of luck, sorry I couldn't have been of more help!