I lack a lot of knowledge surrounding most stuff about linux, but I use a steam deck so it's arch/steamos. When I bought the game, version 0.5.1 worked fine and now that 0.5.2 is out, I tried launching it but it comes up with a Godot error.

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I have a similar issue. Run the executable from the terminal any time you have an issue with something launching. It's a great way for the system to tell you what you need.
Go to file location in your browser, open the terminal from that location, then type:
sudo ./INSERTFILENAMEHERE
It will then run the executable while printing everything that's happening. You can usually fix whatever it is by googling whatever it says is missing and installing the relevant package. In my case it says the program needs GLIBC_2.4.3 which I should have AFAIK. Hopefully yours is easier to fix. I'm on ubuntu so it might be a different issue. In the meantime, just use 0.51 if you can't figure it out.
Bump! I am also having this issue. The Choicer Voicer versions post-0.5.1 seem to want glibc version 2.43, but the newest version available in my NixOS system's package repository is 2.42. I imagine this can be resolved with Godot export settings. True for both "standard" and "compatibility" versions of the game. I'm happy to help test and troubleshoot!