Auto merge of #14024 - meliache:update-split-emacs-documentation, r=lnicola

Update documentation for emacs and split it for LSP-mode and Eglot

Emacs has now two LSP clients, the more minimalistic and lightweight [Eglot](https://joaotavora.github.io/eglot) and the extensive though a bit bloated [LSP Mode](https://github.com/emacs-lsp/lsp-mode). Eglot will soon be shipped with Emacs29. Both have rust-analyzer enabled by default and require no further setup other then being installed and enabled. `lsp-rust.el` is not required anymore.

The base-installation for each of those modes is so easy now that I don't think an enumerated list is necessary, both packages can be installed via the standard `M-x package-install` and the installation is a one-liner that I provide.

Configuration is only necessary for supporting the rust-analyzer extensions to the LSP protocol, which are built into LSP mode and require an [extension-package](https://github.com/nemethf/eglot-x) for Eglot.

But for further documentation, including the LSP extensions, I link against official documentation where possible to avoid duplicating efforts having to continually update this to stay up-to-date.

I rewrote most of the original emacs documentation, but the [linked blog](https://robert.kra.hn/posts/2021-02-07_rust-with-emacs/) post by `@rksm` seems still being actively updated with updates to LSP mode, so I kept the link. That blog post is opinionated, I personally use different packages which achieve similar end results (Eglot instead of LSP-mode, corfu instead of capf, vertico instead of helm etc.). But if someone doesn't already have an extensive Emacs configuration, I think this is not a bad starting point.

Disclaimer: I'm a Rust beginner, which is why I read the rust-analyzer setup docs. So I necessarily know how most Rust experts use Emacs. But I'm an experienced Emacs user who uses several other programming languages via LSP-mode support in Emacs. I used both, initially LSP-mode and recently migrated to Eglot.

Also I'm not an experienced in writing asciidoc and I didn't do a local test-built, hopefully the html builds in the way I imagine it. So I recommend to check that aspect of the PR. Maybe the documentation is in the CI build-artifacts?

This is a duplicate of a PR to the old rust-analyzer project https://github.com/rust-analyzer/rust-analyzer.github.io/pull/197, which I made because I didn't know that the documentation now lives here.

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