I download and run the game itself trough the "Heroic Launcher" as flatpak on my Debian-based distro, and it runs good.
The problem is whenever I save the game nothing happens (at the first phone cell in chapter 1).

When saving the game, it does not respond at all, like I don't get the message that it's done and I have to start the game every time from beginning. I read, that this kind of glitch may occur and I tried it few time with re-installing the game and doing it over and over again, but the game just wont save.

I am not sure, if this post will help you.

I have kind of the same problem in Windows.
Sometimes the game doesn't save, even when I pressed every button correctly.
In this case the message "Save complete" also doesn't appear.

I just try again, and most of the time it works the 2nd time or 3rd time.
But I guess you already tried that.

I will try this on the new installation of Linux. Thanks for your response, I really want to play this game, but sometimes as Linux-gamer it isn't easy and it kinda makes me feel better hearing the problem is not (always) in my OS.

Good that the main problem for Linux also got solved!


Still, my Windows problem might also apply to you:

When saving, pay attention, that the message "Save complete" appears.

If yes, everything is ok.
I no, you have to save again (and again), until the message appears.

It is slightly annoying but not a big problem when you know about this.