If LLVM has a SPIRV backend, probably very little. For a proof of concept, a bachelor CS thesis would probably do.
Clang already has a CUDA parser, and all the code to lower CUDA specific constructs to LLVM-IR, some of which are specific for the PTX backend. If you try to compile CUDA code for a different target, like SPIRV, you'll probably get some errors saying that some of the LLVM-IR instructions generated by clang are not available in that backend, and you'll need to generate the proper SPIRV calls in clang instead.
Its probably a great beginner task to get started with clang and LLVM. You don't need to worry about the C++ frontend side of things because that's already done, and can focus on understanding the LLVM-IR and how to emit it from clang when you already have a proper AST.
Clang already has a CUDA parser, and all the code to lower CUDA specific constructs to LLVM-IR, some of which are specific for the PTX backend. If you try to compile CUDA code for a different target, like SPIRV, you'll probably get some errors saying that some of the LLVM-IR instructions generated by clang are not available in that backend, and you'll need to generate the proper SPIRV calls in clang instead.
Its probably a great beginner task to get started with clang and LLVM. You don't need to worry about the C++ frontend side of things because that's already done, and can focus on understanding the LLVM-IR and how to emit it from clang when you already have a proper AST.