If it does not work, there might be a proven way around this for your issue. My wife is playing on Steam and uses a mix of games either straight through Steam (via Proton) or using CrossOver. For Ubisoft and Blizzard related games she uses CrossOver. For everything else she uses Steam. I installed it on her PC according to instructions and it works fine. Her Linux Mint is based on Ubuntu 22.04 which is what you use. Since I should not use HTML code her I send you (a) the reference link and (b) the steps as plain text here.
The reference URL is: https://www.windowscentral.com/how-install-proton-steam-play-linux
The step by step instructions you find there are as follows:
[ How to install Proton (Steam Play) on Linux ]
To get Steam running on Ubuntu with Proton is an incredibly easy process.
You can install Steam through the Ubuntu Software store app, but I always recommend using the Terminal
where possible in order to learn more about Linux.
One last thing: DON'T use the Flatpak version of Steam else you may encounter some problems. Let's prepare our system and install Steam, which will handle all things Proton.
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To begin, we need to make sure the Ubuntu multiverse repository is enabled:
sudo add-apt-repository multiverse
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Next, we need to update the repositories:
sudo apt-get update
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Finally, we can install Steam:
sudo apt install steam
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Open Steam:
steam
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Enter your Linux user password into the Terminal window.
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Log into Steam using your credentials.
Steam Play uses Proton so all you need to do with Steam installed is to click install on any game
and the client will download all the necessary files. You may need to clear the filter on your library,
which may be excluding all games that don't support Linux natively. Even with the best graphics
card, you will need to ensure Ubuntu is using the latest available drivers.
[ What games work with Proton on Linux? ]
You can check to see what games work with Steam Play and Proton by using the website ProtonDB.
URL: https://www.protondb.com/
Not only will this handy platform inform you as to which games will work on Linux, but it'll also
provide additional details on how well each game works, as well as any additional steps one needs
to take to get everything working.
end of copy
Hope that helps you :)
Hans