Has anyone had any luck replicating their Proton setup outside of Steam? Or simply just running a Proton game outside of Steam after getting it set up using Steam?

I have run many Windows games outside of Steam.

I prefer to set up each one manually: Create a Wine prefix, install the game (or copy it from an existing installation), install a few key libraries like DXVK and a Visual C++ runtime, make a launch script with game-specific environment settings or launch options. Tools like Lutris and Bottles can automate much of this, in case you need a little help or just find a GUI more convenient.

This is my usual approach to non-Steam games (especially GOG), but even Steam games can be convinced to work offline with the help of a Steam emulator. It wouldn't work with a game encumbered by DRM (e.g. Denuvo) unless a cracked version could be located, but in my experience, that's a minority of Steam games that I categorically avoid in the first place.

So, I'm not worried about my game library vanishing if I ever lose access to Steam for whatever reason. Most (if not all) of it could be recovered with a bit of effort.