Based on discussion on the Debian bug tracking system, this is a problem with an incomplete downgrade from the Debian unstable rolling release to the slightly older 'testing' rolling release, and there is nothing that can be done to solve it from Steam's side.
Debian unstable is used to develop the next Debian stable release. It's as unstable as its name indicates, and not all packages will be installable all of the time; this is not a bug.
Debian testing is also used to develop the next Debian stable release, and is also a constantly moving target. It aims to be internally-consistent at all times, but you'll continue to have installability problems after downgrading from unstable to testing, for as long as you have packages from unstable that are strictly newer than the version in testing.
This will resolve itself automatically after a while: specifically, next time the Mesa packages in Debian testing (trixie) get updated, they will be in sync at version 23.3.3-1 or later.
OS: Debian stable = "trixie" amd64
This is not Debian stable. The current stable Debian release is Debian 12 (bookworm).
The current status of trixie is that it is the testing branch. It is expected to become stable in mid 2025, as Debian 13.
There is option to have unstable repo with higher priority than testing, but that is problem with incompatibility with compiled packages and libs with different versions and expectations and crashes will occur. But possible. But another problem is then when testing will be staged into freeze into next cycle, it could take that state a long time and during that time unstable packages could not be existent and in testing it will be as next stable versions, which is huge headache. But this is the Debian Way of Thinking.
Wait for next Proton(WoW64, backends), it is more 32bits unfriendly... on unstable branch... and finding libs like gles, egl should make it libs supportive somehow installable...
Nothing extracted yet.
After a system update both installation methods of Steam fail due to an obolete i386 library version:
Installed: libglapi-mesa:i386 = 23.3.2-2
Required: libglapi-mesa:i386 = 23.2.1-1 -> downgrade breaks Debian/X11/Mesa installation
Installation methods
Your system information
With installation method 1: Debian
apt install steam-installer
apt policy steam-installer libglx0:i386 libglx-mesa0:i386 libgl1-mesa-dri:i386 steam-libs:i386 libglapi-mesa:i386
With installation method 2: Steam
Selecting previously unselected package steam-launcher.
(Reading database ... 1041372 files and directories currently installed.)
Preparing to unpack /tmp/steam_latest.deb ...
Unpacking steam-launcher (1:1.0.0.78) ...
Setting up steam-launcher (1:1.0.0.78) ...
Processing triggers for man-db (2.12.0-1) ...
Processing triggers for hicolor-icon-theme (0.17-2) ...
Processing triggers for mate-menus (1.26.1-1) ...
Processing triggers for desktop-file-utils (0.27-1) ...
Processing triggers for gnome-menus (3.36.0-1.1) ...
Processing triggers for mailcap (3.70+nmu1) ...
steam
Thanks,
Axel Dürrbaum