Hello @koalasbruder, this doesn't read as a steam client issue.
https://packages.ubuntu.com/cosmic/steam exists and there's no particular reason why this would not work.
sudo dpkg --add-architecture i386
sudo apt update
sudo apt install steam
I changed the language from German to English and now it is working.
I don't know why it was not working before.
Closing per the last comment.
I've got exactly the same problem,
using Ubuntu 18.10,
and following the exact sequence of commands proposed above.
But it does not work :
Running Steam on ubuntu 18.10 64-bit
STEAM_RUNTIME is enabled automatically
Pins up-to-date!
/home/$user/.local/share/Steam/steam.sh: line 823: /home/$user/.local/share/Steam/ubuntu12_32/steam-runtime/run.sh: No such file or directory
or
glxChooseVisual failed
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Your system information
Please describe your issue in as much detail as possible:
Cannot install Steam.
Because Ubuntu removed multiarch support if you don't upgraded from 18.04.1 (with multiarch support enabled) to 18.10.
Steps for reproducing this issue: