Hello @VortexV, we've seen this before when some dependency of mesa was updated from a repo source that provides the 64 bit variant of a package, but not the 32 bit variant of the same package. Ubuntu inherits Debian's multiarch requirements that architecture variants of a package (like amd64 and i386) must have exactly the same version and apt strongly dislikes downgrading packages to resolve conflicts.

The general process to troubleshoot this usually involves asking apt to install Steam from the distro repositories (not Snap), finding which package is having a hard time in the output from apt, then inspecting what package versions are installed and available with apt policy and telling apt to install matching 32 bit and 64 bit variants of that package at the same time which will either tell you it can do it or reveal a dependency of that package which you can repeat the process until you find the mismatched versions.

Note: If at any point during troubleshooting this type of issue, if apt asks for permission to remove a bunch of packages do not let it proceed.

For example, let's say apt points towards libgl1-mesa-dri as the package with trouble, then I'd check what versions are installed with apt policy libgl1-mesa-dri libgl1-mesa-dri:i386, then ask apt to install both the 32 bit and 64 bit variant of the mesa OpenGL driver with sudo apt install libgl1-mesa-dri libgl1-mesa-dri:i386 and see what it says.

If you need to downgrade a package, then you first need to consider if it'll cause trouble for some other software that depends on the newer-than-distro-repo package version and if it's acceptable risk, then you tell apt to install exact versions for both the 32 bit and 64 bit variant of that package. (Something like sudo apt install libfakeexample=1.2.3-4 libfakeexample=1.2.3-4:i386.)

Without details, this is a general distro packaging issue, not a Steam issue and the package conflict should be reported to the repo maintainer(s) that provided the package that's giving trouble.