Auto merge of #61407 - phansch:annotate_snippet_refactoring1, r=oli-obk

Add new diagnostic writer using annotate-snippet library

This adds a new diagnostic writer `AnnotateRsEmitterWriter` that uses
the [`annotate-snippet`][as] library to print out the human readable
diagnostics.

The goal of #59346 is to eventually switch over to using the library instead of
maintaining our own diagnostics output.

This PR does **not** add all the required features to the new
diagnostics writer. It is only meant as a starting point so that other
people can start contributing as well.

There are some FIXMEs in `librustc_errors/annotate_rs_emitter.rs` that
point at yet to be implemented features of the new diagnostic emitter, however
those are most likely not exhaustive.

[as]: https://github.com/rust-lang/annotate-snippets-rs

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