Even though Vulkan for would be of little gain for the web due to all the security considerations required, a WebGL backend should still be able to benefit from being built on Vulkan instead.
Due to the refinement of the pipeline and memory access, etc. provided by Vulkan, there's a lot of room for optimization.
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Though on the other hand, even with additional overhead on a Vulkan web API, the improved state management and access to command buffers may still allow for smarter rendering with negligible overhead via JS
Fun times