Slight mistake in your description: CUDA is an out of date API that was replaced by Khronos's own official compute APIs. Khronos is a standards consortium that Nvidia is a founding member of.
Although the marketing department at Nvidia still pushes for greenfield CUDA codebases, no new code should be written in it, and they should opt for open source international standards only. Khronos APIs are implemented by over 120 vendors.
With my past experience in Khronos, NVIDIA is indeed a member and they sent decent guys to the meetings -- but only for strategic reasons, rather than "advocating for open standards" as you described. My experiences there actually told me the opposite that they will never drop CUDA. Objectively they also have incentive to do so: fighting with 100-ish companies to ratify something is always slower than rolling out an feature in an ecosystem you have total control of.
How may standards Khronos endorced over the years/decades on compute? From an uneducated and external view, it seems every 2-5years there is a new standard.
Ultimately 2. OpenCL, and Vulkan (via it's compute shader).
Sycl's job isn't that, its meant to abstract implementations of common components across different kinds of hardware, and doesn't force you into any particular style of impl. As in, I could write a component for Sycl for my GPU in OpenCL and what Sycl would abstract away from the consumer of my component would be the entire usage of OpenCL itself; but I could write a component for a DSP, and it'd use an entirely closed source SDK for that hardware and is entirely opaque, and a Sycl user could use that impl for that function of they owned that DSP (instead of a CPU-based or GPU-based impl).
Also, Vulkan's compute doesn't replace OpenCL (not even in the sense that Vulkan, as a graphics API, replaces OpenGL). They're different levels of abstraction. Most Vulkan games are written almost entirely in compute shaders (ex: the powerhouse that is the Doom 2016 and Doom Eternal engines; and why they perform so fucking amazingly on paltry hardware like the original revision Xbox One, or hell, even the Switch).
In addition, I almost consider DX12 a flavor of Vulkan. Same job, written largely by the same people from the same companies, but instead of being OpenGL C-dialect flavored, its D3D C++-dialect flavored, but they both have entirely equivalent APIs that often call the same driver internals and produce nearly identical MIR. Microsoft did this on purpose to reflect the nature of how modern GPUs are almost entirely software renderers, sans certain parts of the texture units.
Although the marketing department at Nvidia still pushes for greenfield CUDA codebases, no new code should be written in it, and they should opt for open source international standards only. Khronos APIs are implemented by over 120 vendors.