The kernel driver is a rather small piece of the overall puzzle though, itps just the pipe that GPU commands are passed through. The bulk of the GPU driver code (and the majority of its impact on performance) is in the userspace components like the shader compiler and the OpenGL/Vulkan libraries. These are closed source.
The exception to this rule is that the kernel driver is responsible for power management and controls the GPU clocks, but as part of opening up the kernel driver NVIDIA made reclocking available for the fully open driver (nouveau/nvk) to use as well which means the performance differences between the two driver stacks are now down to optimizations.
The only instance I can see this is if a game requires a new Vulkan extension, which wouldn’t need a new kernel but would need a new Mesa version to provide that extension. For the most part, games use established and standardized APIs (OpenGL, Vulkan, Direct3D) to utilize the GPU and as long as the driver implements the APIs used by the game, the driver doesn’t need to continuously update in order to support game updates. On Linux, the driver doesn’t handle Direct3D anyways and an intermediate layer (DXVK or VKD3D) is used to translate Direct3D API calls into the Vulkan API. Vulkan does support extensions which are added every so often to provide new interfaces and the userspace portion of the driver (which is responsible for compiling/translating Vulkan API calls into raw GPU instructions) needs to be updated to support these, but also sometimes these extensions are optional and games can use less optimized code paths to work around missing extensions.