Because you brought up a non-proton related issue. It's highly unlikely this is proton related, this is an issue on how the steam virtual keyboard and Skyrim interact, and since the keyboard doesn't cause issues on any other game I think it's very likely the culprit is Skyrim, and if that's the case I want to know if the issue also happens on Windows.

Is it possible that the issue is within proton? Yes, but the problem you presented can be in multiple other places that proton can't touch. For example if the game crashes on windows too then proton is working correctly, and even if it doesn't it can still be something else besides proton, e.g. steam closing the keyboard in a different manner, Skyrim has had a famous bug where it crashes when you alt+tab away from it and come back on Windows for a long time, and opening a virtual keyboard on top of the game and going back is essentially alt+tabing, so I wouldn't be surprised to find out that this is the same bug in Skyrim showing up with a different face.

PS: out of curiosity I went and loaded my old prisoner save, and named the character which is how many people reported the bug and it just worked, so even if this used to be an issue, doesn't seem like it is anymore.