Add std::autodiff and Rust to the Enzyme CI #145899
Description
std::autodiff is currently not build in CI, which causes unfortunate regressions every once in a while.
Enabling autodiff on nightly would either require approval on the infra side, since the rustc binary would become [larger](#t-infra > MCP - Enable autodiff in CI) on every (supported) platform, or someone would need to implement #143295.
std::autodiff (as well as the upcoming std::batching) is based on https://github.com/enzymead/enzyme, an LLVM incubator project. So a simpler alternative to building Enzyme in the Rust CI would be to build Rust in the Enzyme CI. They have 32 core runners available, so build times should be acceptable. Enzyme currently has integration tests for C++, Julia, and MLIR, so there are plenty of examples to copy. We have build instructions for rustc with std::autodiff enabled in the rustc-dev-guide. As another related example, here is a discussion from the time where we added Rust to the Enzyme compiler explorer: EnzymeAD/enzyme-explorer#15
The goal for now is to just check in the Enzyme CI that the four x.py test autodiff test commands from the dev-guide pass.
I think the task should be sufficiently easy for anyone who previously worked with Docker or the github CI. In the long run we probably want both CIs to build both Enzyme and rustc, but it would be a good improvement for now.
If anyone wants to claim and has question, feel free to either ask them here (and cc @ wsmoses) or create an issue over at https://github.com/EnzymeAD/Enzyme, either works.