First I used Proton GE 8-25, then 8-27, but it didn’t make a difference.
However, I’ve moved the game to my Windows drive in the meantime, and it runs flawlessly there. Which means the problem is not the game itself, so maybe Wine/Proton will be able to fix these issues some day.
(The Spacers Choice Edition Epic gave away some time ago is also fully DRM-free btw. You can run it directly from the executable, no launcher or authentication required. In fact, I’ve found that many of those Epic freebies I got over the last few years are DRM-free. I’m basically a legal, official pirate at that point.)