My experience with running Steam on Debian 13 was different from yours. I don't recall having any issues starting Steam. Unfortunately, I don't recall if I had to do anything unusual other than installing it (from the Debian repos?), but it certainly didn't involve editing any configs. This was a clean Debian 13 install, not an upgrade from 12, and it had almost no other software installed, so I wonder if one of those is a factor.

Regarding the games not working though, I think I may be able to provide some help. I found out from someone I know that just installing Steam and trying to start Windows games is not sufficient. Apparently, for whatever reason the Steam client seems to come with some ancient version of Proton that is not compatible with many (most?) games. You need to also install Proton-GE, which I guess has all the latest compatibility updates. The easiest way to do this is to install ProtonUp-QT, which is a GUI to install and manage Proton-GE, and then from there install the latest Proton-GE. After that, there is one more step that's required, unfortunately. For each game you want to play in Steam using the latest Proton, you need to go into that game's settings in Steam and change the compatibility layer to use the latest Proton and not the built-in one. This is my understanding and this may not be the most efficient way to do all this. After I did all this, the games that weren't starting or were freezing shortly after starting began to work flawlessly. I have no idea why it requires jumping through so many hoops.

A pattern that I believe I noticed but haven't completely confirmed yet is that it seems that the whole Proton-GE rigamarole may only be required for games that don't say that they're "verified" under the steam deck compatibility section on their store page. The games that say they have "verified" compatibility with Steam deck may not require any additional steps. I could be wrong about this too.