I’ve had better luck using the Flatpak version of Steam than either the repo version or downloaded from Steam. On 22.04 I could not get the Gnome launcher to work at all for either and had to use the terminal. No issues using the Flatpak version. It also works with Proton-Up, which is also available as a Flatpak.
As for your issue specifically, you could look at the logs, but the only way I know to do that is via the Terminal, and you mentioned you don’t want to do that.
It will most definitely be logged if it’s Gnome crashing. If the entire system is crashing that’s a very different story, and if you’re hard resetting it sounds like a system crash, not Gnome specifically. Depending on how it crashes, there may be logs.