Auto merge of #101799 - LukeMathWalker:distribute-json-doc, r=jyn514

Distribute json doc

# Overview

We add a new component, `rust-json-docs`, to distribute the JSON version of rustdoc's output for public compiler crates (i.e. `std`, `alloc`, `proc_macro`, `core` and `test`).
As discussed in #101383, we do not bundle this up as part of the existing `rust-docs` component since `rustdoc`'s JSON format is still unstable.

# Open questions / Doubts

I tried my best, but I never touched this codebase and I couldn't find much documentation on how `dist` works - I pattern-matched existing code, which might have led to some non-sensical choices in the eyes of people more familiar with the codebase. In particular, I am not sure if my choice of adding a new config flag is appropriate or if the decision to build/not build the JSON docs is more appropriately gated by one of the existing flags.
Any suggestion is more than welcome.

Closes #101383