Thanks for the screenshots. These games fall back to software rendering which explains the subpar performance. This is why you didn’t see the game process listed as an NVIDIA graphics client in your screenshots.
I’ve been looking at CrossCode which at least seems to be using a Chromium based web engine for rendering and the reason for falling back to software rendering is likely related to that. For example, in 2021, Chromium had known problems finding accelerated NVIDIA drivers under PRIME Render Offload due to strict sandboxing preventing access to some shared libraries. This was fixed, with the final patch going into Chromium source tree in late June 2021.
I have no visibility into CrossCode but maybe the game internally uses (or ends up using externally?) an older Chromium engine that does not have this fix. It’s also possible there are other restrictions (from the execution environment, Chromium, Steam, or something else) limiting what libraries and files the game engine can access. Nevertheless, the end result is that the game does not seem to find NVIDIA userspace drivers for PRIME Render Offload and then fails to initialize OpenGL/Vulkan accelerated graphics.
Based on the data I have so far I can’t tell where the root cause to this lies but it might be a good start to inform the game developer about this so as to at least let them make sure they’ve got this use case covered in their testing.